Journal of information and communication convergence engineering 2017; 15(1): 21-27
Published online March 31, 2017
https://doi.org/10.6109/jicce.2017.15.1.21
© Korea Institute of Information and Communication Engineering
In this research, we study the outage probability for distributed space-time coding-based cooperative (DSTC) systems with amplify-and-forward relaying over Rayleigh fading channels with a high temporal correlation where the direct link between the source and the destination is available. In particular, we derive the upper and lower bounds of the outage probability as well as their corresponding asymptotic expressions. In addition, using only the average channel powers for the source-to-relay and relay-to-destination links, we propose an efficient power allocation scheme between the source and the relay to minimize the asymptotic upper bound of the outage probability. Through a numerical investigation, we verify the analytical expressions as well as the effectiveness of the proposed efficient power allocation. The numerical results show that the lower and upper bounds tightly correspond to the exact outage probability, and the proposed efficient power allocation scheme provides an outage probability similar to that of the optimal power allocation scheme that minimizes the exact outage probability.
Keywords Amplify-and-forward relay, Cooperative systems, Distributed space-time coding, Outage analysis, Power allocation
Node cooperation techniques have attracted considerable attention from the perspective of achieving cooperative diversity. Distributed space-time coding [1] is a node cooperation technique, and distributed space-time coding-based cooperative (DSTC) systems have been well investigated in [2-6]. In [2], the bit error probability has been analyzed for DSTC systems using amplify-and-forward (AF) relaying, and the optimum power allocation for these systems has been presented assuming full instantaneous channel information at the source and the relay. In [3], the outage probability and the diversity–multiplexing tradeoff have been studied for DSTC systems using decode-and-forward relaying. In [4], adaptive buffer-aided DSTC schemes with AF relaying have been proposed, and their bit error probabilities have been investigated. In [5], assuming that instantaneous channel information is available at the relay, power allocation schemes have been proposed for DSTC systems with AF relaying in order to minimize the bit error probability and to maximize the data rate. In [6], using only the average channel power information, the authors have proposed power allocation for DSTC systems with AF relaying to minimize the outage probability, where the direct link between the source and the destination is ignored.
In this paper, we focus on DSTC systems with AF relaying, where the Alamouti code [7, 8] is used for distributed space-time coding. Analogous to previous works, in DSTC systems, two transmission phases are considered as follows: in the first phase, both the relay and the destination receive the original data signals from the source, whereas in the second phase, only the destination receives the space-time coded signals from both the source and the relay.
In practice, a continuous wireless channel between the transmitter and the receiver may have a temporal correlation. Thus, considering highly correlated channels over time, we assume that the channel for the source-to-destination (S-D) link is constant during two phases.
In this study, we analyze the outage probability for DSTC systems with AF relaying over Rayleigh fading channels with a high temporal correlation, where the direct line between the source and the destination is assumed to be available unlike in the system model considered in [6]. However, unfortunately, it is expression for the exact outage probability. Thus, we derive the upper and lower bounds of the outage probability as well as their corresponding asymptotic expressions. Further, in previous works, instantaneous channel information was required for power allocation. However, assuming that only the average channel power for the source-to-relay (S-R) and relay-to-destination (R-D) links is known at the source and the relay, we propose a scheme for efficient power allocation between the source and the relay to minimize the asymptotic upper bound of the outage probability, and verify the effectiveness of this scheme. We do so by comparing the outage performances and the proposed and the optimal power allocation scheme that minimizes the exact outage probability.
We consider a DSTC system consisting of three single-antenna nodes: a source, a relay, and a destination. As shown in Fig. 1, in the DSTC system, the source broadcasts signals to both the relay and the destination during the first time slot, and then, the relay and the source collaboratively transmit space-time coded signals to the destination over the second time slot. We assume perfect synchronization between the cooperative transmissions in the second time slot. After the destination receives the signals over the two time slots, it combines them using maximal ratio combining (MRC).
In this study, we focus on an AF relay, and thus, the space-time coded signals transmitted by the relay are generated from the noisy signals received from the source.
Further, the AF relay uses variable amplification for preventing the saturation of the relay amplifier and satisfying its transmit power constraint. We assume that the relay has the exact channel information for the S-R link, and the destination has the exact channel information for all the links, i.e., the S-D link, the S-R link, and the R-D link.
In the DSTC system, assuming that the channels are constant during a time slot, the complex channels for the S-D and S-R links in the first time slot are denoted by
Let
During the first time slot, the source sequentially transmits two complex symbols
for
Then, at the destination, the received DSTC signals are decoupled as follows:
Finally, the destination combines the decoupled signals and the preceding received signals by using MRC as follows:
for
Letting
where
The MRC output SNR in (9) is upper bounded as follows:
Further, a lower bound on the MRC output SNR is given as follows:
The outage probability is defined as the probability that the achievable data rate, (1/2)log2(1+
where
Using (10) and the PDFs in (12), we obtain a lower bound on the outage probability for the DSTC system as follows:
For high transmit SNRs (i.e.,
Let
Further, the PDF of
Using (14),
Let
When
From (18) and (19), the diversity order for the DSTC system is obtained as follows:
where
In this section, assuming that only the average channel powers for the S-R and R-D links are known at the source and the relay, we propose an efficient power allocation scheme to improve the outage performance of the DSTC system. The efficient power allocation coefficients denoted by
Inserting
Taking the derivative of
Using (22), we can derive the equation
From (23),
where 0 <
To show that
In this section, we verify the analytical expressions for the lower and upper bounds on the outage probability in (13) and (17), respectively, as well as their corresponding asymptotic expressions in (18) and (19) by comparing with the simulation results of the exact outage probability. In addition, we verify the effectiveness of the proposed efficient power allocation scheme by comparing the simulation results of the exact outage probabilities for the optimal and the proposed power allocation schemes.
Figs. 2 and 3 show the upper and lower bounds on the outage probability of the DSTC system as well as their asymptotic results for
Fig. 4 shows the exact outage probability and the asymptotic upper bound on the outage probability for power allocation between the source and the relay when
Fig. 5 compares the exact outage probabilities for the optimal power allocation scheme and the proposed efficient power allocation scheme when
In this paper, we presented closed-form expressions for the lower and upper bounds on the outage probability for a DSTC system with AF relaying over Rayleigh fading channels with a high temporal correlation, which tightly correspond with the exact outage probability. Further, we provided the asymptotic expressions for the lower and upper bounds. In addition, a scheme for efficient power allocation using only the average channel powers for the source-to-relay and relay-to-destination links at the source and the relay is proposed to minimize the asymptotic upper bound of the outage probability. Numerical results show that the proposed efficient power allocation scheme achieves an outage performance similar to that of the optimal power allocation scheme.
received his B.S., M.S., and Ph.D. in Electrical Engineering from Hanyang University, Ansan, Korea, in 2003, 2005, and 2008, respectively. He worked towards LTE-Advanced standardization at Samsung Electronics Co. from 2008 to 2010. He was a Post-Doctoral Fellow at the Department of Electrical Engineering, Hanyang University, Ansan, Korea, from April 2010 to March 2011. Since March 2011, he has been with the Department of Electrical, Electronic, and Control Engineering, Hankyong National University, Anseong, Korea. Further, since February 2017, he has been a visiting associate professor in the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada. His present research interests include non-orthogonal multiple access, millimeter-wave wireless communications, cooperative communications, multi-hop relaying, transmission and reception of multiple-input and multiple-output communications, multicast communications, and multi-user channel state information feedback.
Journal of information and communication convergence engineering 2017; 15(1): 21-27
Published online March 31, 2017 https://doi.org/10.6109/jicce.2017.15.1.21
Copyright © Korea Institute of Information and Communication Engineering.
In-Ho Lee
University of British Columbia and Hankyong National University
In this research, we study the outage probability for distributed space-time coding-based cooperative (DSTC) systems with amplify-and-forward relaying over Rayleigh fading channels with a high temporal correlation where the direct link between the source and the destination is available. In particular, we derive the upper and lower bounds of the outage probability as well as their corresponding asymptotic expressions. In addition, using only the average channel powers for the source-to-relay and relay-to-destination links, we propose an efficient power allocation scheme between the source and the relay to minimize the asymptotic upper bound of the outage probability. Through a numerical investigation, we verify the analytical expressions as well as the effectiveness of the proposed efficient power allocation. The numerical results show that the lower and upper bounds tightly correspond to the exact outage probability, and the proposed efficient power allocation scheme provides an outage probability similar to that of the optimal power allocation scheme that minimizes the exact outage probability.
Keywords: Amplify-and-forward relay, Cooperative systems, Distributed space-time coding, Outage analysis, Power allocation
Node cooperation techniques have attracted considerable attention from the perspective of achieving cooperative diversity. Distributed space-time coding [1] is a node cooperation technique, and distributed space-time coding-based cooperative (DSTC) systems have been well investigated in [2-6]. In [2], the bit error probability has been analyzed for DSTC systems using amplify-and-forward (AF) relaying, and the optimum power allocation for these systems has been presented assuming full instantaneous channel information at the source and the relay. In [3], the outage probability and the diversity–multiplexing tradeoff have been studied for DSTC systems using decode-and-forward relaying. In [4], adaptive buffer-aided DSTC schemes with AF relaying have been proposed, and their bit error probabilities have been investigated. In [5], assuming that instantaneous channel information is available at the relay, power allocation schemes have been proposed for DSTC systems with AF relaying in order to minimize the bit error probability and to maximize the data rate. In [6], using only the average channel power information, the authors have proposed power allocation for DSTC systems with AF relaying to minimize the outage probability, where the direct link between the source and the destination is ignored.
In this paper, we focus on DSTC systems with AF relaying, where the Alamouti code [7, 8] is used for distributed space-time coding. Analogous to previous works, in DSTC systems, two transmission phases are considered as follows: in the first phase, both the relay and the destination receive the original data signals from the source, whereas in the second phase, only the destination receives the space-time coded signals from both the source and the relay.
In practice, a continuous wireless channel between the transmitter and the receiver may have a temporal correlation. Thus, considering highly correlated channels over time, we assume that the channel for the source-to-destination (S-D) link is constant during two phases.
In this study, we analyze the outage probability for DSTC systems with AF relaying over Rayleigh fading channels with a high temporal correlation, where the direct line between the source and the destination is assumed to be available unlike in the system model considered in [6]. However, unfortunately, it is expression for the exact outage probability. Thus, we derive the upper and lower bounds of the outage probability as well as their corresponding asymptotic expressions. Further, in previous works, instantaneous channel information was required for power allocation. However, assuming that only the average channel power for the source-to-relay (S-R) and relay-to-destination (R-D) links is known at the source and the relay, we propose a scheme for efficient power allocation between the source and the relay to minimize the asymptotic upper bound of the outage probability, and verify the effectiveness of this scheme. We do so by comparing the outage performances and the proposed and the optimal power allocation scheme that minimizes the exact outage probability.
We consider a DSTC system consisting of three single-antenna nodes: a source, a relay, and a destination. As shown in Fig. 1, in the DSTC system, the source broadcasts signals to both the relay and the destination during the first time slot, and then, the relay and the source collaboratively transmit space-time coded signals to the destination over the second time slot. We assume perfect synchronization between the cooperative transmissions in the second time slot. After the destination receives the signals over the two time slots, it combines them using maximal ratio combining (MRC).
In this study, we focus on an AF relay, and thus, the space-time coded signals transmitted by the relay are generated from the noisy signals received from the source.
Further, the AF relay uses variable amplification for preventing the saturation of the relay amplifier and satisfying its transmit power constraint. We assume that the relay has the exact channel information for the S-R link, and the destination has the exact channel information for all the links, i.e., the S-D link, the S-R link, and the R-D link.
In the DSTC system, assuming that the channels are constant during a time slot, the complex channels for the S-D and S-R links in the first time slot are denoted by
Let
During the first time slot, the source sequentially transmits two complex symbols
for
Then, at the destination, the received DSTC signals are decoupled as follows:
Finally, the destination combines the decoupled signals and the preceding received signals by using MRC as follows:
for
Letting
where
The MRC output SNR in (9) is upper bounded as follows:
Further, a lower bound on the MRC output SNR is given as follows:
The outage probability is defined as the probability that the achievable data rate, (1/2)log2(1+
where
Using (10) and the PDFs in (12), we obtain a lower bound on the outage probability for the DSTC system as follows:
For high transmit SNRs (i.e.,
Let
Further, the PDF of
Using (14),
Let
When
From (18) and (19), the diversity order for the DSTC system is obtained as follows:
where
In this section, assuming that only the average channel powers for the S-R and R-D links are known at the source and the relay, we propose an efficient power allocation scheme to improve the outage performance of the DSTC system. The efficient power allocation coefficients denoted by
Inserting
Taking the derivative of
Using (22), we can derive the equation
From (23),
where 0 <
To show that
In this section, we verify the analytical expressions for the lower and upper bounds on the outage probability in (13) and (17), respectively, as well as their corresponding asymptotic expressions in (18) and (19) by comparing with the simulation results of the exact outage probability. In addition, we verify the effectiveness of the proposed efficient power allocation scheme by comparing the simulation results of the exact outage probabilities for the optimal and the proposed power allocation schemes.
Figs. 2 and 3 show the upper and lower bounds on the outage probability of the DSTC system as well as their asymptotic results for
Fig. 4 shows the exact outage probability and the asymptotic upper bound on the outage probability for power allocation between the source and the relay when
Fig. 5 compares the exact outage probabilities for the optimal power allocation scheme and the proposed efficient power allocation scheme when
In this paper, we presented closed-form expressions for the lower and upper bounds on the outage probability for a DSTC system with AF relaying over Rayleigh fading channels with a high temporal correlation, which tightly correspond with the exact outage probability. Further, we provided the asymptotic expressions for the lower and upper bounds. In addition, a scheme for efficient power allocation using only the average channel powers for the source-to-relay and relay-to-destination links at the source and the relay is proposed to minimize the asymptotic upper bound of the outage probability. Numerical results show that the proposed efficient power allocation scheme achieves an outage performance similar to that of the optimal power allocation scheme.
Han-Gyeol Lee, Duckdong Hwang, and Jingon Joung
Journal of information and communication convergence engineering 2024; 22(4): 267-272 https://doi.org/10.56977/jicce.2024.22.4.267