IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 7, JULY 2011
707
Selective Decode-and-Forward Using Fixed Relays and Packet Accumulation Hirley Alves and Richard Demo Souza
Abstract—We propose a cooperative scheme using a fixed relay based on the selective decode-and-forward (SDF) protocol. The relay accumulates 𝑍 source packets, concatenates them into a single packet, and forwards this single packet to the destination with an increased spectral efficiency. The proposed scheme can considerably outperform the conventional SDF protocol, at the cost of a moderate increased maximum delay. Index Terms—Cooperative diversity, selective decode-andforward.
I. I NTRODUCTION NE of the most efficient cooperative protocols is the Selective Decode-and-Forward (SDF) [1], in which the relay forwards the source message only if that is free of errors. However, with half-duplex radios the SDF protocol suffers from a multiplexing loss, since the relay has to listen the source in a first time slot and then retransmit that message in a second slot. In [2], a multiple relay selection protocol is proposed in order to mitigate such multiplexing loss. A return channel is assumed for the selection of the best relay. In [3], [4] protocols using two relays are introduced, where in [3] repetition coding is employed with Bell Labs Layered SpaceTime detection, while in [4] cooperative space-time coding is used. Some of the multiplexing loss is recovered by [2]–[4], but by using multiple relays and complex coding schemes. In this work we propose a simple technique that can recover a good amount of the multiplexing loss. The scheme is based on the SDF protocol, but here a fixed relay accumulates 𝑍 packets, concatenates them and forwards a single packet to the destination by using an increased spectral efficiency. The proposed scheme considerably outperforms the conventional SDF protocol. The method takes advantage of the much reduced path loss in the relay to destination channel in case of fixed relays. Moreover, in such a scenario multiple relays are usually not available, and then the solutions proposed in [2]–[4] can not be successfully applied. The rest of this paper is organized as follows. In Section II we introduce the system model, while in Section III the outage and throughput analysis are presented. Numerical results are shown in Section IV and Section V concludes the paper.
O
II. S YSTEM M ODEL Consider three half-duplex nodes, source (S), relay (R) and destination (D), in a circular cell of radius 𝜌. Node D is a Manuscript received February 24, 2011. The associate editor coordinating the review of this letter and approving it for publication was W. Zhang. The authors are with CPGEI, Federal University of Technology - Paraná (UTFPR), Curitiba, PR 80230-901, Brazil (e-mail:
[email protected],
[email protected]). This work was partially supported by CNPq and CAPES (Brazil). Digital Object Identifier 10.1109/LCOMM.2011.050311.110416
base station located on the center, while S is a user located at the border of the cell. Node R is a fixed device, deployed by the service provider, and it is located between S and D, at distances 𝑑 from S and 𝑟 from D. Following [5], the antennas of both R and D are at a higher height, and we assume that there is some line of sight (LOS) in the R-D link, while the S-R and S-D links are in non-line of sight (NLOS). We use the Walfisch-Ikegami (WI) large scale path loss model, with the parameters suggested in [6]. Moreover, all channels are subject to Gaussian noise with variance 𝑁0 /2 per dimension, while the fading is modeled by a Nakagami-m distribution. For NLOS we use 𝑚 = 1, which is equivalent to Rayleigh fading, while for LOS we use 𝑚 = 2, which is less severe. The proposed method can be summarized as: i) R listens the channel until the 𝑍-th packet from S arrives; ii) R retransmits a unique packet to D containing the data of all packets from S successfully decoded at R. Since R utilizes a single packet (with the same duration as a packet from S), it has to use a spectral efficiency which is 𝑘 times that of S, where 𝑘 ∈ [1, 𝑍] is the number of packets correctly decoded at R. Such increased spectral efficiency can be obtained, for instance, by data compression, a higher modulation order, a higher channel coding rate, or a combination of all of them. In addition, D employs selection combining. Next, the proposed method is characterized in terms of throughput, which is defined as the average spectral efficiency seen by D after decoding. III. O UTAGE AND T HROUGHPUT A NALYSIS A data packet x𝑧 is broadcasted by S and is heard at D and R. The signal received at D is: √ (1) ySD,𝑧 = 𝑃S /𝛾SD ℎSD,𝑧 x𝑧 + wSD,𝑧 , where 𝑃S is the source transmit power, 𝛾SD is the path loss between S and D, ℎSD,𝑧 is the Nakagami-m fading coefficient between the two nodes, and wSD,𝑧 is the noise vector. An outage event occurs when the signal-to-noise ratio (SNR) at D falls below a threshold 𝛽 [1]. The SNR in the S-D link is: ∣ℎSD,𝑧 ∣2 𝑃S , (2) 𝛾SD 𝑁 where 𝑁 = 𝑁0 𝐵, 𝑁0 is the noise power spectral density per Hertz and 𝐵 is the bandwidth, in Hertz. In this case, the outage probability in the S-D link after the 𝑧-th transmission is [7]: ( ) 𝑚𝑁 (2RS −1)𝛾SD Ψ 𝑚, 𝑃S , (3) 𝑝SD = 𝑃 𝑟{SNRSD,𝑧 < 𝛽S } = Γ (𝑚 − 1) SNRSD,𝑧 =
where 𝛽S ∫= 2𝑅S − 1, 𝑅S is the source spectral efficiency, 𝑏 𝑏) = 0 𝑦 𝑎−1 exp(−𝑦)𝑑𝑦 is the incomplete and Γ(𝑎) = ∫Ψ(𝑎, ∞ 𝑎 𝑦 exp(−𝑦)𝑑𝑦 is the complete gamma function. 0
c 2011 IEEE 1089-7798/11$25.00 ⃝
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IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 7, JULY 2011
2
where 𝛾SR is the path loss, ℎSR,𝑧 is the fading, and wSR,𝑧 ∣ℎ ∣2 𝑃S is noise. The SNR is SNRSR,𝑧 = SR,𝑧 𝛾SR 𝑁 , and the outage probability 𝑝SR is equal to (3) but replacing 𝛾SD by 𝛾SR . Note that 𝑝SR < 𝑝SD since 𝑑 < 𝜌 and due to the antenna heights. Suppose that 𝑍 packets were sent from S to R and D. Then R forwards to D a single packet xˆ , where the spectral efficiency depends on how many out of the 𝑍 packets could be decoded at R. The signal received at D from R is: √ (5) yRD = 𝑃R /𝛾RD ℎRD xˆ + wRD , where 𝑃R is the relay transmit power, ℎRD is the Nakagami-m fading, and wRD is the noise vector. The outage probability of the R-D link is: ( ) 𝑚𝑁 (2RR −1)𝛾RD Ψ 𝑚, 𝑃R 𝑝RD,𝑛 = , (6) Γ (𝑚 − 1) where 𝑅R = 𝑘𝑅S is the relay spectral efficiency. For determining the throughput of the proposed scheme, all the combinations of the number of packets (out of 𝑍) that can be decoded at R and D, after the transmission from S, have to be taken into account. Moreover, one has to consider if the packets that could be correctly decoded at R and at D are the same or not. Node R can only be of help if it decodes packets that could not have been decoded at D after the transmission from S. When one consider all these possibilities, a general expression for the throughput can be given by (9), where 𝑗 is the number of packets correctly decoded at D after the transmission of 𝑍 packets from S, and 𝑘 is defined as before. Coefficient 𝒞𝑗,𝑘,𝑍 takes into account all the combinations of correctly decoded packets at both D and R, and is: ⎧ 𝑘 = 𝑗, ⎨𝑓 (𝑗, 𝑘, 𝑍) 𝑘 > 𝑗, 𝒞𝑗,𝑘,𝑍 = 𝑔(𝑗, 𝑘, 𝑍) ⎩ 𝑅S ⋅(𝑗+1) [(𝑍 ) ( 𝑗 )] 𝑅S ⋅𝑗 ( 𝑗 ) ⋅
𝑍+1
𝑘
−
+
𝑘
𝑍+1
⋅
𝑘
𝑘 < 𝑗, 𝑍 ≥ 3,
(7) where 𝑓 (𝑗, 𝑘, 𝑍) is as (10) and 𝑔(𝑗, 𝑘, 𝑍) is calculated as: ⎧ 𝑅S ⋅(𝑘+1) 𝑅S ⋅𝑘 𝑘 = 1, 𝑍 < 3 𝑍+1 + 𝑍+1 ⎨ ⎩
𝑅S ⋅(𝑘+1) 𝑍+1 𝑅S ⋅(𝑘+1) 𝑍+1
⋅ ⋅
(𝑍−1) 𝑘 [(𝑍 ) 𝑘
+
𝑅S ⋅𝑘 𝑍+1
⋅
[(𝑍 )
]
𝑘
− (𝑍 − 𝑗) +
−
(𝑍−1)]
𝑅S ⋅𝑘 𝑍+1
𝑘
⋅ (𝑍 − 𝑗)
𝑗 = 1, 𝑍 ≥ 3 𝑗 > 1, 𝑍 ≥ 3
(8) When 𝑍 = 1 the proposed method reduces to the conventional SDF, so that the throughput is simply: 𝑍=1 𝒯CT =
𝑅S 𝑅S (1 − 𝑝SD ) + 𝑝SD (1 − 𝑝SR ) (1 − 𝑝RD,1 ) . 2 2
In case of 𝑍 = 2:
(11)
[ 2𝑅S 2𝑅S (1 − 𝑝SD )2 + (𝑝SD )2 𝑝SR (1 − 𝑝SR ) 3 3 ] 2𝑅S 2 (1 − 𝑝SR ) (1 − 𝑝RD,2 ) + 2 ⋅ 𝑝SD (1 − 𝑝RD,1 ) + 3 [ 2𝑅S 𝑅S (𝑝SR )2 + (1 − 𝑝SR )2 (1 − 𝑝RD,2 ) (1 − 𝑝SD ) 3 3 ] ( ) 2𝑅S 𝑅S (12) + + 𝑝SR (1 − 𝑝SR ) (1 − 𝑝RD,1 ) . 3 3
𝑍=2 𝒯CT =
1.8
(4)
1.6 1.4
Throughput (bits/s)
By its turn, the signal received at the relay is: √ ySR,𝑧 = 𝑃S /𝛾SR ℎSR,𝑧 x𝑧 + wSR,𝑧 ,
1.2 1 0.8
nCT CT Z=1 CT Z=1 Simulation CT Z=2 CT Z=2 Simulation CT Z=3 CT Z=3 Simulation CT Z=4 CT Z=4 Simulation
0.6 0.4 0.2 0 −15
−10
−5
0
5
10
15
20
25
30
SNRSD (dB)
Fig. 1. Throughput of the non-cooperative (nCT) and the cooperative (CT) schemes, as a function of SNR, when 𝑅S = 2bps/Hz.
Finally, the overall outage probability of the non-cooperative (nCT) method is equal to (3), while the throughput is: 𝒯nCT
=
𝑅S ⋅ (1 − 𝑝SD ) .
(13)
IV. N UMERICAL R ESULTS We consider 𝑁 = −174dBm/Hz, 𝐵 = 1.25MHz, 𝑍 ∈ {1, 2, 3, 4}, and that S, R and D antenna heights are 1.5, 30 and 30m, respectively. We first compare the nCT to the proposed cooperative (CT) scheme, considering 𝑅S = 2bits/s/Hz, and that R is positioned as in [8]. Fig. 1 presents the theoretical and the simulated results, obtained by the Monte Carlo method, which agree very well. We can see that the nCT scheme achieves a larger maximum throughput, whereas the proposed scheme achieves a maximum throughput between the conventional SDF (𝑍 = 1) and the nCT scheme. The proposed scheme outperforms the conventional SDF protocol in the whole SNR range, while the larger is the number of accumulated packets 𝑍 the larger is the throughput. Fig. 2 shows the throughput as a function of the spectral efficiency, considering SNRSD = 0dB and SNRSD = 20dB. For SNRSD = 0dB the proposed scheme highly outperforms the nCT scheme, whereas at SNRSD = 20dB the proposed scheme has only a small advantage. From the figure it is also clear that there is a spectral efficiency which maximizes the throughput for each value of SNR, for each scheme. We present in Fig. 3 the throughput as a function of SNR, taking into account the optimal spectral efficiency for each scheme for each SNR value. One can see that our proposed method presents a great advantage at low and medium SNR over the nCT scheme, recovering a good amount of the multiplexing loss, and that it always outperforms the conventional SDF protocol (𝑍 = 1). Considering the whole SNR range, we can say that 𝑍 = 2 is the best option for the proposed scheme, even though 𝑍 = 3 is slightly better at the low SNR range. By further increasing 𝑍 we are not able to improve performance.
ALVES and SOUZA: SELECTIVE DECODE-AND-FORWARD USING FIXED RELAYS AND PACKET ACCUMULATION
𝑍 𝒯𝐶𝑇 =
𝑍⋅𝑅S 𝑍+1
(𝑍 ) 𝑖⋅𝑅S (𝑍 ) ∑ ∑ 𝑍−𝑖 (1 − 𝑝SD )𝑍 + (𝑝SD )𝑍 𝑍 (1 − 𝑝SR )𝑖 (1 − 𝑝RD,𝑖 ) + 𝑍−1 (𝑝SD )𝑍−𝑗 (1 − 𝑝SD )𝑗 × 𝑖=1 𝑖 𝑍+1 (𝑝SR ) 𝑗=1 𝑗 } { ∑ 𝑍−1 𝑍−𝑘 𝑗⋅𝑅S S (𝑝SR )𝑍 + 𝑍⋅𝑅 (1 − 𝑝SR )𝑍 (1 − 𝑝RD,𝑍 ) + (1 − 𝑝SR )𝑘 (1 − 𝑝RD,𝑘 ) 𝑘=1 𝒞𝑗,𝑘,𝑍 (𝑝SR ) 𝑍+1 𝑍+1
⎧ 𝑅S ⋅(𝑘+1) 𝑅S ⋅ (𝑍 − 𝑘) + 𝑍+1 ⎨ 𝑍+1 [( ) ] 𝑅S ⋅𝑍 𝑅S ⋅𝑗 ⋅ 𝑍𝑘 − 1 + 𝑍+1 𝑓 (𝑗, 𝑘, 𝑍) = 𝑍+1 ( ⎩ 𝑅S ⋅min{𝑍,𝑗+𝑘} ⋅ 𝑍−𝑘) + 𝑅S ⋅(min{𝑍,𝑗+𝑘}−1) ⋅ [(𝑍 ) − (𝑍−𝑘) − 1] + 𝑘 𝑘 𝑘 𝑍+1 𝑍+1
SNR
=0dB
SNR
SD
4.5 7
4
0.5
3 2.5 2 1.5 1 0.5
2 4 6 Spectral Efficiency (bits/s/Hz)
Throughtput (bits/s/Hz)
1
6
3.5 Throughput (bits/s/Hz)
Throughput (bits/s/Hz)
nCT CT Z=1 CT Z=1 Simulation CT Z=2 CT Z=2 Simulation CT Z=3 CT Z=3 Simulation
0 0
(9)
𝑗 = 1, 𝑘 = 1 𝑘 =𝑍−1 𝑅S ⋅𝑘 𝑍+1
(10)
1
