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Variable packet splitting transmission in multirelay cooperative communications with DF and DAF for SCFDMA
EURASIP Journal on Wireless Communications and Networking volume 2013, Article number: 64 (2013)
Abstract
In recent years, cooperative communications are widely studied. Cooperative communications can obtain the space diversity as multipleinput multipleoutput (MIMO) systems. In cooperative communications, the relay method is important as decodeandforward (DF) and decodeamplifyforward (DAF). The multirelay cooperative communications can improve the system performance. In the multirelay cooperative communications, the optimum packet splitting method is effective. Moreover, the multirelay cooperative communications can more improve the system performance by using the power allocation (PA). However, the PA method requires large feedback information (FBI). To solve this problem, in this article, we propose the optimum packet splitting method based on the time domain channel state information (CSI) in the multirelay cooperative communication with DF and DAF.
Introduction
As the next generation standard of the mobile communications, a longterm evolution (LTE)Advanced is standardized [1]. LTEAdvanced supports broadband data services with the maximum transmission rate of about 0.1–1 Gbps. In a LTEAdvanced, single carrier frequency division multiple access (SCFDMA) has been adopt in the uplink communication, and orthogonal frequency division multiple access (OFDMA) has been adopt in the downlink communication [2]. SCFDMA can achieve a low peak average power ratio (PAPR) compared with OFDMA [3–5]. Since a low PAPR of SCFDMA can reduce the cost and the power consumption of communication, SCFDMA is suitable transmission method for the uplink communication.
In recent years, cooperative communications are widely studied [6–9]. Cooperative communications use the relay node except the source and destination nodes. By using the relay node, cooperative communications can obtain the space diversity as multipleinput multipleoutput (MIMO) systems. For the problem of PAPR, the signals of each antenna have to process in the same device for MIMO systems. As a result, MIMO systems increase PAPR. On the other hand, the signals process in the independent device as the relay node for cooperative communications. Therefore, cooperative communications mitigate the problem of PAPR compared with MIMO systems [10, 11]. In cooperative communications, the relay method is important as amplifyandforward (AF), decodeandforward (DF), and decodeamplifyforward (DAF) [12–21]. AF is the simplest method. This is because it is only adjust the amplitude of the signal in the relay node [12–14]. However, since AF is poor in a frequency selective fading environment, the system performance is significantly degraded. To solve this problem, DF and DAF have been proposed [15–21]. DF and DAF detect the received signal in the relay node. As a result, DF and DAF are strong in a frequency selective fading environment. For the deference of DF and DAF, DF detects the received signal by using the hard decision [15, 16]. On the other hand, DAF detects the received signal by using the soft decision [17–21]. In this article, we use DF and DAF, and compare their performances.
In cooperative communications, the multirelay cooperative communications have been proposed [22]. This system can improve the system performance to obtain more strong diversity by using several relay nodes. However, if the channel condition of relays is bad, the system performance is degraded. To solve this problem, the optimum packet splitting has been proposed in MIMO systems [23]. The optimum packet splitting method splits the packet by considering the channel condition and sends from each transmit antenna. As a result, the optimum packet splitting method can improve the system performance. However, the optimum packet splitting is not considered in the multirelay cooperative communications. Therefore, in this article, we propose the optimum packet splitting in the multirelay cooperative communication systems. Cooperative communications can improve the system performance by using the power allocation (PA) [24–28]. This method is also effective in the multirelay cooperative communications [26]. Therefore, [27] has adopt the waterfilling power allocation (WF/PA) method. The WF/PA method mitigates the deep faded channel by using the optimum power [24–27]. However, the PA method requires large feedback information (FBI) since it has to feedback the channel state information (CSI) of each sampling point in a frequency domain. To solve these problems, in this article, we propose the optimum packet splitting method based on the time domain CSI in the multirelay cooperative communication with DF and DAF.
Common notations that E·, (·)^{∗} denote the ensemble average operation, a complex conjugate, respectively.
System model
In this article, we assume the multirelay cooperative communications as shown in Figure 1. Here, we define the notation as follows.

SD is the link between the source and destination nodes.

SR is the link between the source and relay nodes.

RD is the link between the relay and destination nodes.

SRD is the link between the source, relay, and destination nodes.
Channel model
We assume that a propagation channel consists of L discrete paths with different time delays. The impulse response h_{ n }(τ,t) for the n th node is represented as
where h_{n,l}, τ_{n,l} are the complex channel gain and the time delay of the l th propagation path for the n th node, and $\sum _{l=0}^{L1}E\left{h}_{n,l}^{2}\right=1$, respectively. The channel transfer function H_{ n }(f,t) is the Fourier transform of h_{ n }(τ,t), and is given by
Source node
The source node block diagram of the proposed system is shown in Figure 2a. Firstly, the coded data is modulated, and is performed with interleaving. After the N_{ c }points IFFT operation, the time domain transmitted signal for the n th node s_{ n }(t) can be expressed as
where N_{ c }is the number of sampling points, T_{ s }is the effective symbol length, and E_{ s }is the average transmission power, respectively. For Equation (3), by using the N_{ c }points FFT operation, the frequency domain signal u_{ n }(k) is given by
where d_{ n }(t) is the original signal for the n th node. From Equation (3), the proposed method splits the packet as shown in Figure 3. Here, the number of total data symbols N_{ d }is defined as
where N_{ d }is the number of data symbols for SD, N_{i,R}is the number of data symbols for i th SRD, and N is the number of relay nodes, respectively. In this article, since we assume the multirelay cooperative communications, we define N_{ D }≥1 and N_{i,R}≥1. For the proposed packet splitting method, we explain in the next section. In general, the guard interval (GI) is inserted in order to eliminate the intersymbol interference (ISI) due to a multipath fading, and hence, we have
where T_{ g }is the GI length.
Relay node
The relay node structure is illustrated in Figure 2b. The received signal for the n th relay node ${\widehat{r}}_{n}\left(t\right)$ can be expressed as
where n_{ n }(t) is additive white Gaussian noise (AWGN) with a single sided power spectral density of N_{0}. After removing the GI, by using the N_{ c }points FFT operation, Equation (7) is rewritten as
where ${\widehat{n}}_{n}\left(k\right)$ is AWGN noise with zeromean and a variance of 2N_{0}/T_{ s }. By using the minimum mean square error (MMSE) equalization, the detected signal of Equation (8) ${\xfb}_{n}\left(k\right)$ is given by
where ω_{n,s r}(k) is the MMSE weight. After the detection, the detected signal ${\xfb}_{n}\left(k\right)$ is also modulated and transmits to the destination node by using decodeandforward (DF) or decodeamplifyforward (DAF).
Destination node
The destination node structure is illustrated in Figure 2c. The received signal r(t) can be expressed as
where r_{0}(t) is the received signal for SD, r_{ n }(t) is the n th received signal for RD, and n(t) is AWGN, respectively. After removing the GI, by using the N_{ c }points FFT operation, Equation (10) is rewritten as
where $\widehat{n}\left(k\right)$ is AWGN noise. By using the MMSE equalization, the detected signal of Equation (11) ${\u0169}_{n}\left(k\right)$ is given by
where ω_{ s d }(k) and ω_{n,r d}(k) are the MMSE weights for SD and n th RD, respectively. Finally, by using the N_{ c }points IFFT operation, the desired signal ${\stackrel{~}{d}}_{n}\left(t\right)$ is given by
MMSE equalization
In this article, we assume the perfect channel estimation. The MMSE weight ω_{ n }(k) is given by
where ${\sigma}_{n}^{2}$ is the noise power [29].
Proposed variable splitting method
In this section, we explain the waterfilling power allocation (WF/PA) method and the proposed variable splitting method.
Waterfilling power allocation (WF/PA)
The waterfilling power allocation (WF/PA) method has been proposed to improve the system performance [24–27]. The WF/PA method mitigates the deep faded channel by using the optimum power assignment. The optimum power of the k th sampling point for the n th node P_{ n }(k) is given by
where the cutoff SNR revel μ_{ n } is
From Equation (15), the WF/PA method can improve the system performance. However, the WF/PA method requires large feedback information (FBI). To mitigate this problem, we propose the variable splitting method.
Proposed variable splitting method
The proposed variable splitting method is performed based on the time domain CSI. For the time domain CSI, the amplitudes are constant. From this characteristic, since FBI of the proposed method becomes only one, the proposed method can reduce FBI compared with the WF/PA method.
Next, we explain the proposed method. The output signal X due to a Rayleigh fading is expressed as
where X_{ c }is a real part and X_{ s }is a imaginary part, respectively [30]. From Equation (17), the amplitude of X is given by
By using Equation (18), the proposed method is performed. First, we define the amplitude for each propagation. The amplitude for SD (λ_{ D }) is expressed as
where X_{ S D } is the output signal due to a Rayleigh fading for SD. Also, the amplitude for the i th SRD (λ_{i,R}) is expressed as
where X_{i,S R}and X_{i,R D}are the output signals due to a Rayleigh fading for i th SR and i th RD, and α is the selection parameter for SRD, respectively. Then, we decide the number of data symbols for SD (N_{ d }) and the number of data symbols for i th SRD (N_{i,R}). Firstly, the proposed method decides the number of data symbols for SD (N_{ d }) as
where γ is the selection parameter for SD and SRD, and ⌊x⌋ stands for the integer and closer to x, respectively. For the parameters α and γ, we decide them by using the computer simulation for DF and DAF in the next section. After choosing N_{ d }, the proposed method decides the number of data symbols for i th SRD (N_{i,R}). The number of data symbols for i th SRD (N_{i,R}) is given by
By using Equations (21) and (22), the proposed method can achieve the optimum packet splitting.
Computer simulation results
In this section, we show the performance of the proposed method. In our simulation, we have used MATLAB simulation. For increasing the simulation accuracy, we consider the Monte Carlo method for computer simulation. Figure 2 shows a simulation model of the proposed system. On the source node, the data stream is encoded. Here, convolutional codes (rate R = 1/2, constrain length $\mathcal{K}=7$) with interleaving are used. The coded bits are QPSK modulated. After serial to parallel (S/P) converted, the FFT spreading operation is performed. By using the IFFT operation, the SCFDM time domain signal is generated and is inserted a guard interval (GI). The SCFDM time domain signal is split based on Equations (21) and (22), and is transmitted to the relay and destination nodes. In this simulation, we assume that the channel estimation is the perfect. Moreover, the SCFDM symbol period is 2 μ s, the GI length is 125 ns, the path separation is T_{path} = 37 ns, and the maximum Doppler frequency is 5 Hz. In the relay node, the received signal is detected as Equation (9). After the detection, the detected signal is modulated again, and is transmitted to the destination node. For the relay method, in this article, we assume the decodedandforward (DF) and the decodeamplifyforward (DAF). In the destination node, all received signals are combined, and are S/P converted. After removing the GI, the parallel sequences are passed to the FFT operator and convert the signal back to the frequency domain. The frequency domain data signal is detected by using the MMSE equalization. After the detection, the detected signal is converted to the time domain signal by the IFFT operation. And then, the total bits are decoded by using the Viterbi soft decoding algorithm. The packet consists of N_{ d }= 80 data symbols. Table 1 shows the simulation parameters.
First, we decide the optimum value of the parameters α and γ for DF. Figure 4 shows the BER versus the parameter α for γ = 0.1, 1, 2, 3, and 4 with E_{ b }/N_{0} = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance. Moreover, when α = 0.1 and γ = 4, the proposed method shows the best BER performance. Figure 5 shows the BER versus the parameter γ for α = 0, 0.1, 0.2, 0.3, and 0.4 with E_{ b }/N_{0} = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance. Moreover, when α = 0.1 and γ = 4, the proposed method shows the best BER performance as same Figure 4. On the other hand, when γ is greater than 4, the proposed method shows the bad BER performance. From Figures 4 and 5, we decide the parameters as α = 0.1 and γ = 4 for DF.
Next, we decide the optimum value of the parameters α and γ for DAF. Figure 6 shows the BER versus the parameter α for γ = 0.1, 1, 2, 3, and 4 with E_{ b }/N_{0} = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance. Moreover, when α = 0.4 and γ = 3, the proposed method shows the best BER performance. Figure 7 shows the BER versus the parameter γ for α = 0, 0.1, 0.2, 0.3, and 0.4 with E_{ b }/N_{0} = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance as same Figure 5. Moreover, when α = 0.4 and γ = 3.5, the proposed method shows the best BER performance. On the other hand, when γ is greater than 3.5, the proposed method shows the bad BER performance. From Figures 6 and 7, we decide the parameters as α = 0.4 and γ = 3.5 for DAF.
Finally, we show the BER performance of the proposed method. Figure 8 shows the BER of the conventional and proposed methods at Doppler frequency of 5 Hz. First, the BER of the conventional method N_{ D }= 40 and N_{i,R}= 20 shows about 4 dB gain compared with N = 0, where i = 1,2. This is because the conventional method of N_{ D }= 40 and N_{i,R}= 20 obtains the strong space diversity by using two relay nodes. Next, the BER of WF/PA shows about 2 dB gain compared with N_{ D }= 40 and N_{i,R}= 20. This is because the WF/PA method mitigates the deep faded channel by using the optimum power assignment. However, the WF/PA method requires large FBI. The proposed method reduces FBI compared with the WF/PA method. Moreover, the BER of the proposed method shows about 2 dB gain compared with the WF/PA method. This is because the proposed method obtains the space diversity and coding gains by using the optimum packet splitting. Finally, we compare the BER performance for DF and DAF. For the conventional and proposed methods, the BER of DAF shows the good BER performance compared with DF. This is because the signal with DAF can obtain the more accurate detected signal compared with DF in the relay node. Moreover, the BER of the proposed method for DAF shows about 1.5 dB gain compared with DF. Therefore, the proposed method for DAF is effective, and shows the best BER performance.
Conclusion
In this article, we have proposed the variable packet splitting method in the multirelay cooperative communications with DF and DAF. The proposed method obtains the space diversity by using the multirelay cooperative communications. Moreover, since the proposed method uses the error correcting code and interleaving, obtains also the coding gain. However, if the channel condition of relays is bad, the system performance is degraded. Therefore, the proposed method splits the packet to obtain the space and coding gains. Moreover, the proposed method uses the selection parameters α and γ to obtain the maximum gains. As a result, the proposed method obtains the maximum coding gain due to the space diversity. From the simulation results, the proposed method has decided the optimum value of selection parameters α and γ, and achieved the best BER performance. Moreover, the proposed method of DAF has shown the good BER performance compared with DF.
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Keywords
 SCFDMA
 Cooperative communications
 Multirelay
 Decodeandforward
 Decodeamplifyforward
 Variable packet splitting