Abstract—In this paper, we propose a new adaptive relaying protocol called Threshold-based Adaptive Decode-Amplify-Forward relaying protocol (T-ADAF). In our protocol, the relay compares the signal to noise ratio (SNR) of the received signal to the average SNR of the source-relay link. If the SNR of the received signal is greater than the average SNR of the source-relay link, then the relay performs the Amplify-Forward relaying protocol (AF). On the other hand, if the SNR of the received signal does not exceed the average SNR of the source-relay link, then the relay performs the Adaptive Decode-Forward relaying protocol (ADF). The performance of the proposed protocol is investigated and a closed form of its symbol error probability is derived in the presence of Rayleigh fading channels. Furthermore, a comparison with other relaying protocols such as AF, ADF and SNR-HDAF (SNR-based Hybrid Decode-Amplify-Forward) is made in order to evaluate the performance of our protocol and to show its benefits. We also investigate the T-ADAF protocol with multiple relays and we derived a closed form of its symbol error probability.
The challenging nature of the wireless channel causes fading to the signal. Cooperative diversity has emerged as a promising technique to combat fading in wireless communications [1], [2]. In fact, cooperative protocols are based on the broadcast nature of the wireless medium and allow users to benefit from spatial diversity by letting nodes transmit multiple independent copies of the same information symbols to the receiver.1
Two basic cooperative strategies have been proposed in the literature [3], [4], [5]: Decode-Forward (DF) and Amplify-Forward (AF). In DF scheme, the relay receives and detects the source message and forwards it to the destination. In AF scheme, the relay simply amplifies the received signal and forwards it to the destination. We can classify the DF strategy as: 1) Fixed Decode-Forward (FDF) where the relay decodes and forwards always the received symbol and 2) Adaptive Decode -Forward relaying (ADF) where the relay forwards the received symbol only when it is properly decoded. AF is the
This work was supported by Qatar National Research Fund under Grant NPRP 08-577-2-241 and NSERC-DG
protocol with the lowest complexity as it does not require decoding at the relays. But its major drawback is the noise amplification. ADF ensures better performances than the AF and FDF protocols in terms of symbol (or frame) error probability. Some cooperative protocols, that take advantages of both AF and ADF protocols, have been proposed in [6], [7]. According to these protocols, the relay performs a soft decoding and forwards the reliability information at the output of its decoder to the destination.
Some new adaptive relaying protocols have been proposed in [8], [9]. In [8], the authors propose that the relay performs either ADF or AF based on the result of the decoding process. If the decoding process succeeds, then the relay regenerates the symbol and retransmits it (ADF mode), whereas if the decoding process fails, then it forwards the signal to the destination instead of remaining silent during the second hop (AF mode). However, the protocol proposed in [8] presents a major disadvantage as the relay has always to decode the received signal in order decide which technique to perform (AF or ADF). It is known that amplifying is simpler than decoding, and hence it is better to define a new criterion to adequately select AF or ADF.
In [9], authors proposed that the used protocol at the relay is chosen based on the SNR of its received signal. The proposed protocol is called SNR-based Hybrid Decode-Amplify-Forward (SNR-HDAF). For SNR-HDAF, the relay performs ADF relaying when the SNR of the received signal is greater than a fixed threshold and performs AF in the other case. However, when the source-relay link is in a “good state”, it is better to amplify the received signal since it is not corrupted. In order to solve these problems, we propose, in this paper, a novel adaptive relaying protocol where the relay compares the measured SNR of the received signal to the average SNR of the source-relay link in order to decide which protocol to perform. The novelty of our protocol is that, contrarily to SNR-HDAF, the relay performs the AF protocol if the measured SNR is greater than the average SNR of the source-relay link and performs the ADF protocol if the measured SNR is lower than the average SNR of the source-relay link. It can be observed that our protocol makes smarter relaying decision than [9] as is it based on a threshold which depends on the state of the source-relay link. This adaptive threshold gives flexibility to the relay to perform the most
appropriate protocol based on the state of the link. We will show along this paper that our protocol outperforms the AF and SNR-HDAF protocols, in terms of symbol error probability, and has the same performances as the ADF protocol in high SNR regime.
The paper is organized as follows. In section II, we investigate the scenario of T-ADAF with one relay and we derive a closed form of its symbol error probability in the high SNR regime. In section III, we study the performances of T-ADAF relaying protocol with multiple relays and we derive an approximation of its SEP in the high SNR regime. Finally, section IV concludes the paper.
II. ONE RELAY SCENARIO
A. System model
We consider a cooperative system with three wireless nodes: a source S, a destination D and a relay R. The system is assumed to be half duplex where the nodes cannot transmit and receive simultaneously. In phase 1, the source S broadcasts its information to both the destination D and the relay R. The received signals �� and �� at the destination and the relay, respectively, can be written as
�� �� �� (1)
and
�� �� �� (2)
where is the transmitted symbol from S with an average energy equal to �, �� and �� are the coefficient of S-R and S-D channels respectively, �� and �� are complex additive white noise with zero mean and variance �.
In phase 2, if the SNR of the signal received at the relay exceeds the average SNR of the S-R link, the relay amplifies the received signal and forwards it to the destination (AF mode). On the other hand, if the channel between the source and the relay suffers from a severe fading such that the SNR falls below the average SNR of the S-R link, the relay tries to decode the received symbol (ADF mode). If the decoding process succeeds, the relay regenerates the symbol and forwards it. Otherwise, the relay remains silent.
Depending on the relaying operation during the second-hop transmission, the received signals at the destination are given as follows
• If �� ��
�� ��
�� �� �� (3)
• If and the symbol is correctly decoded
�� ���
�� �� (4)
where �� is the instantaneous SNR of a-b link. �� is the channel gain of R-D link
and �� is a complex additive white noise with zero mean and variance �. ��, �� and �� are modeled as zero-mean, complex Gaussian random variables with variances �� ��
and �� respectively. �� �� �� , where �� is the
distance between a and b �� and is the path-loss exponent. The noise terms �� �� and �� are assumed to be independent and identically distributed (i.i.d). is the amplification gain when AF mode is active and it is formulated as
�
���
� �
(5)
If the relay performs the AF protocol ( �� �� , then the instantaneous SNR of the maximum ratio combining (MRC) output, according to [10], is given by
������ ��
��������
��������� (6)
When the DF protocol is performed ( �� �� , the instantaneous SNR of the MRC output can be written as follows: • If the received symbol is correctly decoded
������ �,���
�� �� (7)
• If the received symbol is incorrectly decoded
������ �,���
�� (8)
In the high SNR regime, ������ �� can be bounded using the
harmonic mean of two independent exponentially distributed random variables [10]
������ ��
�� (9)
where Z is defined by: �� ��
�� ��
(10)
B. Symbol error probability
In this section, we derive the performance of the proposed protocol in terms of SEP. We calculate a closed-form expression for symbol error probability for the single relay scenario for M-ary phase shift keying (M-PSK) modulations. The average SEP can be expressed as [11]
�
�
�
����
�
(11)
where � is the moment-generating function (MGF) of defined as
� � (12)
where � is the expectation operator over the random variable . The average symbol error probability of T-ADAF protocol can be written as
������ �� �� ������ ��
�� ��
������ �,���
������ �,���
(13)
726
where • �� �� is the probability that the measured SNR
at the relay is greater than the average SNR of the S-R link.
• �� �� is the probability that the measured SNR at the relay is less than the average SNR of the S-R link.
• is the SEP at the relay. • ������
�� is the SEP at the destination if the relay decides to amplify and forward what it has received from the source.
• ������ �,��� is the SEP at the destination when the
relay has correctly decoded the received symbol. • ������
�,��� is the SEP at the destination if the relay decides to remain silent.
�� �� and �� �� can be written respectively as
�� �� ���
∞
���������
(14)
�� �� . (15)
The expression of is given by [12]
���
���������
�
�
�
���������
�
����
����
(16)
After developing (16), the final expression of can be expressed as
��
�
�
��
�
�
����
�
(17)
The average error probability ������ �,��� is given by
������ �,���
���
�
�
����
�
���
�
�
(18)
where ���et ���
are the MGF functions of �� and �� respectively
�����
(19)
where
The average error probability ������ �,��� is given by
������ �,���
���
�
�
����
�
(20)
The average error probability ������ �� is given by
������ ��
�
�
� ���
�
�
����
�
(21)
where � is the MGF of Z when �� ��. � is computed numerically using the Laplace Transform of the PDF of Z which is derived in the appendix. We can obtain numerically the SEP at the relay by replacing (17), (18), (20) and (21) into (13).
C. Numerical results
In this section, we provide numerical and simulation results in order to show and validate the performances of our proposed protocol. We compare the T-ADAF protocol with AF, DF and SNR-HDAF in terms of SEP. For AF, we also display the SEP curves given by equations [8, Eq19] and [10, Eq20]. For ADF protocol, we display the SEP curves given by [8, Eq11]. For the SNR-HDAF protocol, we display the curve obtained by simulation for a threshold T = 20 dB.
Fig. 1, Fig. 2, and Fig. 3 show the SEP versus the SNR for quadrature phase shift keying (QPSK) modulation versus transmit power � � . The path-loss exponent was set to 3. In Fig.1, we have taken into account a symmetric system where the S-R and the R-D distances are equal ( �� ��
. We can see in Fig. 1 that the T-ADAF protocol outperforms AF and SNR-HDAF and achieves almost the same performances as ADF.
Fig.1. SEP of the different protocols in the presence of a single relay
�� ��
When the relay is located far from the source (Fig. 2), the performances of the four protocols are worse than their symmetric system’s performances. As in the symmetric system, the T-ADAF protocol outperforms the AF and
DF (Analytical)
AF (Analytical)
T-ADAF (Analytical)
SNR-HDAF (Simulation)
ADF (Analytical)
E1/N0 E1/N0 (dB)
727
SNR-HDAF protocols and achieves nearly the same performances as ADF. When the relay moves close to the source, the results presented in Fig. 3 show that the four protocols offer the same performance. It is obvious from these figures that the performances depends on the relative distance of the relay and that the scenario with the relay placed halfway between the source and the destination, achieves the best performances in terms of SEP.
Fig.2. SEP of the different protocols in the presence of a single relay
�� ��
Fig.3. SEP of the different protocols in the presence of a single relay
�� ��
III. MULTIPLE RELAYS SCENARIO
In this section, we extend our work to the scenario of multiple relays. We analyze the performance of our protocol in terms of SEP considering M-PSK modulation.
A. System Model
We consider the cooperative relay-based wireless system with N+2 nodes: one source S, N relays and one destination D. The source broadcasts the signal in the first-hop. Then, each relay compares the SNR of the received signal with the average SNR of its corresponding S-R link. Among the N relays, p relays decide to perform AF. The N-p remaining relays proceed with ADF relaying. So they decode the
received symbol. q among them succeed in the decoding process. The remaining N-p-q relays remain silent. In the AF mode, the received signal from the source-relay link is forwarded to the destination with an amplifying parameter �, k = 1, . . . , N. Finally, the destination combines the received signals using the MRC technique to enhance the reliability.
Fig.4. T-ADAF with N relays
We denote � as the set of p relays which perform AF relaying and � as the set of q relays with ��,� ��,� , (k = 1, . . . , N) which successfully decodes the symbol. Upon receiving the source signal, each relay in � will simply amplify the received signals from the source and each relay in
� will forward the modulated symbol to the destination.
The received signals at the destination and the k-th relay, respectively, during the broadcasting phase, are given by
�� �� �� (22)
and ��,� ��,� ��,� (23)
where is the transmitted symbol from the source with an average energy equal to �.
Let ��, �, represent the received signal at the destination from the j-th relay. Hence, ��, can be expressed as
��, ��, ��, ��, (24)
where is the amplification factor. It is given by:
�,
��,
�
� �
(25)
Let ��,! � , represent the received signal at the destination from the i-th relay. Hence, ��,! can be expressed as
where �� ��,� and ��,� represent the channel fading coefficients which are modeled as in the one relay scenario. While, ��, ��,� and ��,� are i.i.d. complex zero-mean white Gaussian noise with variance �.
AF(Théorique)
DF(Théorique)
HDAF(Théorique)
DF (Analytical)
AF (Analytical)
T-ADAF (Analytical)
SNR-HDAF (Simulation)
ADF (Analytical)
P1/N0 E1/N0 E1/N0 (dB)
DF (Analytical)
AF (Analytical)
T-ADAF (Analytical)
SNR-HDAF (Simulation)
ADF (Analytical)
P1/N0 E1/N0 E1/N0 (dB)
��,! ��,! ��,! (26)
hSR,N
hRD,p
hSR,1
hRD,p+q hSR,p+q
hSD
hSR,p
Rp+q
1
S
Rp
RN
hRD,N
hRD,1
R1
D
728
In our analysis, we assume that the amount of energy consumed by relays which participate in the relaying phase is the same amount of energy consumed by the source during the broadcasting phase. Assuming that there are p performing AF and q relays successfully decoding the symbol in the first hop, then each relay will consume �,� � during the relaying phase. The instantaneous SNR of the MRC output is given by
������"�#�$%&�� ��,!
!∊�(
��, ��,
��, ��, ∊�)
(27)
where �� is the instantaneous SNR of S-D link, ��,� is the instantaneous SNR of k-th relay-to-destination link and ��,� is the instantaneous SNR of source-to- k-th relay link. Regarding the third term in (27), it can be tightly bounded in the form of harmonic mean of two independent and exponentially distributed random variables [11]
������_+_�,�-./ �� ��,!
!∊�(
∊�)
(28)
where
��, ��,
��, ��,
(29)
B. Symbol error probability
In this section, we drive closed-form expression of the SEP for M-PSK modulation.
Let �,� represent the set of relays which have been selected to participate in the relaying phase. The probability that �,� is selected is given by
�,� ��, ��,0
∊�)
(30) ��,! ��,1 !
!∊�(
��,� ��,� �
�∉�)
�∉�(
where �, ��,! ��,1 and ��, ��,0 are defined similarly to the one relay scenario given in Section II.B. Hence, the average SEP in this protocol can be expressed as
������_+_�,�-./
(31) �,�
�(�)
���
�
�
����
�
���3
�
� �4
�
�
∊�)!∊�(
where ��� ���3 �4are the MGF functions of ��,
��,! and respectively. The probability density function (PDF) of is derived in the Appendix.
C. Numerical results
In order to evaluate the performances of the proposed protocol, we provide numerical results and plot the SEP for QPSK modulation versus � �. The relays are placed halfway between the source and the destination ��,�
��,� . The path-loss exponent was set to 3. We display the SEP curves given by (31) for different number of relays (N=1, 2, 3, 4, 5). Examining the curves in Fig. 5, we can see that the performance of T-ADAF improves as the number of relays increases. We notice that the proposed protocol offers a diversity order equal to N+1.
IV. CONCLUSION
In this paper we have proposed a Threshold-based Adaptive Decode-Amplify-Forward relaying protocol. We have studied the scenario with single relay and derived a closed form of its SEP expression. We also compared the SEP performance of the AF, DF, SNR-HDAF and T-ADAF protocols. It has been shown that the T-ADAF protocol outperforms the AF and SNR-HDAF protocols and achieves almost the same performances as ADF in the high SNR regime. It has been shown also that the SEP depends on the relay’s location and that the best performances are achieved when the relay is located half-way between the source and the destination. We have also investigated the SEP of T-ADAF relay protocol with multiple relays. It has been shown that the performance of the proposed protocol improves when the number of relays increases.
Fig.5. Symbol error probability for QPSK modulation versus � � in symmetric cooperative system with multiple relays
APPENDIX
The CDF of Z can be given by:
��� ��
�� ��
A.1
E1/N0 (dB)
729
��� ����
��
����� ��
��� 5����5
�
���
�
���������
���5
����5 .
We have �� �� as the relay is operating in the AF mode. Then the CDF can be written as follows
���
A.2
�
���������
65
6�5
6
���������
∞
��������� .
Tacking the differentiation in with respect to z, the PDF of Z is given by
��� ��
�
�
7
���������
A.3
�� ��
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