Security-reliability performance of cognitive AF relay-based wireless communication system with channel estimation error
© Gu et al.; licensee Springer. 2014
Received: 23 November 2013
Accepted: 29 January 2014
Published: 5 March 2014
In this paper, both the security and the reliability performance of the cognitive amplify-and-forward (AF) relay system are analyzed in the presence of the channel estimation error. The security and the reliability performance are represented by the outage probability and the intercept probability, respectively. Instead of perfect channel state information (CSI) predominantly assumed in the literature, a certain channel estimation algorithm and the influence of the corresponding channel estimation error are considered in this study. Specifically, linear minimum mean square error estimation (LMMSE) is utilized by the destination node and the eavesdropper node to obtain the CSI, and the closed form for the outage probability and that for the intercept probability are derived with the channel estimation error. It is shown that the transmission security (reliability) can be improved by loosening the reliability (security) requirement. Moreover, we compare the security and reliability performance of this relay-based cognitive radio system with those of the direct communication system without relay. Interestingly, it is found that the AF relay-based system has less reliability performance than the direct cognitive radio system; however, it can lower the sum of the outage probability and the intercept probability than the direct communication system. It is also found that there exists an optimal training number to minimize the sum of the outage probability and the intercept probability.
Nowadays, the increasing demand for high data rate wireless access and services brings about the problem of spectrum scarcity . Cognitive radio (CR) [2, 3] has been recognized as a promising technology to improve spectrum utilization efficiency and solve the spectrum scarcity problem. CR can enable unlicensed users, also referred to as cognitive users or secondary users, to communicate with each other over licensed bands. FCC  gives a formal definition of CR: ‘A cognitive radio is a radio that can change its transmitter parameters based on interaction with the environment it operates’.
Typically, a cognitive transmission process consists of two essential phases: spectrum sensing phase and data transmission phase. In the spectrum sensing phase, cognitive users attempt to find the spectrum hole, which is a frequency band assigned to the primary users but is not being utilized by the users at a particular time and specific geographic location . The spectrum hole is typically located through the following techniques: energy detection , matched filter, and cyclostationary detection . In the data transmission phase, cognitive users transmit data to each other through the detected spectrum hole. Different transmission techniques have been studied in [8–11] and references therein.
Due to the broadcasting nature of wireless channel and the openness of cognitive radio architecture where various unknown wireless devices are allowed to access the licensed spectrum, cognitive radio systems face a challenge of physical layer security. For example, one receiver located near the cognitive source can receive the signal from it and recover the original information.
Much attention has been given to physical layer security in wireless communication systems [12–14]. It is Wyner who firstly investigated the physical-layer security problem in an information-theoretic sense  in 1975. Shortly after, the authors in  extended Wyner’s results to Gaussian wiretap channels and derived the secrecy capacity. In recent years, a multiple-input single-output (MISO) wiretap channel is considered in , and a multiple-input multiple-output (MIMO) wiretap channel is studied in . Besides, cooperative relay-aided secure communication has been suggested in . Furthermore, the authors in  characterize the security-reliability trade-off performance of conventional direct transmission from source to destination in the presence of an eavesdropper, where the security and reliability are evaluated by the intercept probability at the eavesdropper and the outage probability at the destination, respectively.
All the previous works for traditional point-to-point networks [12–14] and relay-based systems [17–19] about secure wireless communication assumed perfect channel state information (CSI). However, in a practical situation, perfect CSI cannot be obtained. For most practical wireless communication systems, training symbols are transmitted so that the receiver can estimate the channel .
Almost in every situation, channel estimation error exists. To our best knowledge, secure wireless communication for relay-based networks has not been addressed in the case of the presence of channel estimation error, which motivates our present work.
In this paper, we study the security and reliability performance of the cognitive amplify-and-forward (AF) relay system in the presence of channel estimation error, and we compare its performance with that of the direct communication cognitive radio system. Specifically, we assume that all communication systems utilize linear minimum mean square error estimation (LMMSE) to obtain channel parameters and derive the corresponding channel estimation error. Based on channel estimates, the detection of data symbols can be found and the channel capacity in the presence of channel estimation error can be obtained. Next, we derive the outage probability and the intercept probability to evaluate the reliability and security performance, respectively. We find that the transmission security (reliability) can be improved by loosening the reliability (security) requirement. Moreover, comparing the security and the reliability performance of this relay-based system with those of the direct communication system without relay, we find that the AF relay-based system has less reliability performance than the direct system; however, it can lower the sum of the outage probability and the intercept probability than the direct communication system. We also show that there exists an optimal training number to minimize the sum of the outage probability and the intercept probability.
This paper is organized as follows: Section 2 gives the system model and Section 3 shows the sensing performance of the cognitive system. Next, the capacity analysis in the presence of channel estimation error is presented in Section 4. The security and the reliability performance are analyzed in Section 5, and numerical results are provided in Section 6 to corroborate our proposed studies. Finally, Section 7 concludes the paper.
2 System model
The transmission process involves two phases. In the first phase, the source node broadcasts signals to the relay node and the destination node; in the second phase, the relay node employs the amplify-and-forward (AF) protocol to resend the received signal to the destination node. That is, the relay node amplifies its received signal with a constant factor α and then forwards it to the destination.
Suppose the subslot transmitted from the source contains N symbols that consist of K training symbols p(n) and M data symbols s(n), as shown in Figure 2. Clearly, N=K+M. Let denote the index set of the training symbols while denote as the index set of data symbols. The full time index set is then .
Let H p represent whether or not there is a spectrum hole for the current time slot. Specifically, H p =H0 represents that a spectrum hole is available, i.e., the channel is unoccupied by the primary users; otherwise, H p =H1. Without loss of generality, we suppose PU1 is transmitting signal x p (n) to PU2 in the case of H p =H1. As did in , we model H p as a Bernoulli random variable with parameter P ∅ (the probability of the channel being available for secondary users), i.e., Pr(H p =H0)=P ∅ and Pr(H p =H1)=1−P ∅ .
Let represent the sensing decision by the source node, i.e., or .
List of the channel notations
Channel from source to destination
Channel from source to relay
Channel from relay to destination
Channel from source to eavesdropper
Channel from relay to eavesdropper
Channel from PU1 to source
Channel from PU1 to relay
Channel from PU1 to destination
Channel from PU1 to eavesdropper
At the beginning of each slot, the source will sense the licensed channel and decide its existence or not. If it decides , then the source will transmit N symbols to the relay and the destination, and next the relay will forward the received N symbols to the destination.
and θ(n) is the signal transmitted from the PU defined in (2).
3 Sensing performance
4 Channel capacity with estimation error
In this section, the channel estimation and data detection process at the destination and also at the eavesdropper are analyzed. The LMMSE method is chosen due to its optimal estimation performance for Gaussian signals . Based on the analysis of estimation and detection process, the mathematical expressions for channel capacity with estimation error are derived.
The source will begin transmission in the two cases of : one is that it successfully detects the existence of the spectrum hole when there is no transmission between the primary users; the other is that it mistakenly detects the appearance of the spectrum hole when the primary users are communicating. In the former case, the nodes in the cognitive system can communicate without any interference from the primary users. Suppose the achievable channel capacity in this case is CI. In the latter case, both PU1, the cognitive source and the cognitive relay will transmit signals and will interfere with each other. In such case, the cognitive system can also obtain certain channel capacity CII. However, the capacity gain is limited and negligible especially when P p , the transmission power of PU1, is high . Thus, in the following capacity analysis, we focus on the first case.
4.1 Signal processing at destination
4.1.1 The first phase
4.1.2 The second phase
Suppose y2p=p H d2p and define the combined channel hsrd=hsrhrd. Clearly, the mean of hsrd is zero and the variance of hsrd is σ srd2=σ sr2σ rd2.
This will guarantee that the interference which resulted from the channel estimation error can be translated into a sort of noise independent from the source signals , which will facilitate the capacity analysis in the following part.
4.1.3 Channel capacity
where P f is the false alarm probability defined in (17) and P d is the detection probability defined in (19). The approximation is due to that CII represents the channel capacity in the case that the cognitive users mistakenly detect the appearance of the spectrum hole when the primary users are communicating. In such case, both PU1, the cognitive source, and the cognitive relay will interfere with each other, which will result in a small value of CII as in [21, 26]. Moreover, we can adjust the threshold so that the detection probability P d can approach 1. Therefore, the item (1−P ∅ )(1−P d )CII in (40) is negligible.
4.2 Signal processing at the eavesdropper
Since the eavesdropper will take a similar estimation and detection process as the destination, the process is described briefly in this subsection.
4.2.1 The first phase
4.2.2 The second phase
Define the combined channel gsre=hsrgre. Clearly, E(gsre)=0 and the variance of gsre is σ sre2=σ sr2σ re2.
4.2.3 Channel capacity
5 Security-reliability performance
5.1 Outage probability
5.2 Intercept probability
where γ e =α2P r P s /Nsre.
5.4 Comparison with direct channel
where . Please refer to  for the detailed derivation process.
Note that the sum of the outage probability and the intercept probability can be considered as a parameter to measure the overall performance. It needs to be pointed out that the strictly mathematical proof of the two propositions is challenging; however, they can be numerically verified through computer simulationsa.
6 Simulation results
In this section, we numerically evaluate both the security and reliability performance of the cognitive relay system with channel estimation error. Let us fix the slot length Lslot=1,000 and sensing duration S=2 and choose the threshold of the energy detector λED=9.2 so that the false alarm probability in (17) P f =0.01.
This paper evaluated both the security and the reliability performance of the cognitive amplify-and-forward (AF) relay system in the presence of the channel estimation error. Specifically, LMMSE is utilized by the destination node and the eavesdropper node to obtain the CSI, and the closed form for the outage probability and that for the intercept probability are derived. Based on these, the security and the reliability performance were evaluated in the form of the outage probability and the intercept probability, respectively. It was shown that the transmission security (reliability) could be improved by loosening the reliability (security) requirement. Moreover, the security and the reliability performance of this relay-based system were compared with those of the direct communication system without relay. Interestingly, it was found that the AF relay-based system has less reliability performance than the direct system; however, it can lower the sum of the outage probability and the intercept probability than the direct system. It was also found that there exists an optimal training number to minimize the sum of the outage probability and the intercept probability.
a This is the reason for the name of proposition, instead of theorem.
This study is supported in part by the Key Laboratory of Universal Wireless Communications, Ministry of Education, China. This study is also supported in part by the National Natural Science Foundation of China (No. 61201202, No. 61372116, and No. 61071077) and by Tsinghua-Tencent Joint Laboratory for Internet Innovation Technology.
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