Originally posted in Sec-IG blog (link to the original post)
Pin-Hsun Lin and Eduard A. Jorswieck
Dresden University of Technology, Germany
Due to the broadcast nature of wireless networks, communications are potentially subject to attacks, such as passive eavesdropping or active jamming. Instead of using the traditional cryptographic approaches  to combat the malicious users, we consider the information-theoretic secrecy. Note that the information-theoretic secrecy approach, initiated by Shannon  and developed by Wyner , can exploit the randomness of the wireless channels to ensure the secrecy of the transmitted messages while there is no assumption on the computation capabilities at the malicious users. As a performance measure for communication systems with secrecy constraints, a secrecy rate is defined as a rate at which the message can be transmitted reliably and securely between the legitimate nodes. However, similar to communication networks without secrecy constraints, the overall performance is limited by the relative channel qualities to guarantee secure communications. Many signal processing and multi-user techniques have therefore been proposed to overcome this limitation such as the use of multiple antennas.
Recently, there has been a substantial interest in the secrecy of multi-user systems , with a particular emphasis on potential cooperation between users to enhance the secrecy of communications. Cooperation in communication networks is an emerging technique to improve the reliability of wireless communication systems, and it involves multiple parties assisting each other in the transmission of messages, see e.g., . Assuming that the cooperative node(s) can be trusted and that they aim at increasing the secrecy of the original transmission in the presence of a possible external eavesdropper, several cooperative strategies have been proposed. As one kind of cooperative communications schemes, cognitive radio technology has been proposed by Mitola in  as an efficient way to enhance the spectrum efficiency which has considerable development over the last few decades. The concept of cooperation for secrecy, and the corresponding cooperative techniques can naturally be applied to the cognitive radio network.
In this article, we consider a cognitive radio (CR) network including four single-antenna half-duplex nodes, where the CR receiver is treated as a potential eavesdropper with respect to the primary transmission . In exchange for cooperation from the CR user to improve/maintain his own secrecy rate, the primary user allows the CR user to share part of the spectrum. Compared to some important literature in this research line, e.g., , , and , etc., we additionally consider the following secure coexistence conditions:
(i) the transmission of CR transmitter does not degrade the primary user’s secrecy rate, and
(ii) the encoder and decoder at the primary transmitter and receiver, respectively, are left intact whether CR transmits or not.
The reasons to consider the secure coexistence conditions are twofold. First, to utilize the time-frequency slot in the overlay sense, cognitive radio systems are obligated not to interfere the primary systems, which is common in cognitive radio systems design. Second, with the condition (ii), cognitive radios are backward compatible with the legacy systems, which cannot sense and adapt to the environment agilely. This conditions make the cognitive radio capable of operating in broader usage scenarios. One of the possible practical scenarios of the considered model is that, the primary users belong to a licensed system, who sells rights of the spectrum usage to a femtocell system. Here we can let the CR transmitter and receiver be the femtocell base station and users, respectively. However, the femtocell operator may not be able to guarantee that the femtocell users are malicious or not. Thus, to provide a secrecy transmission to the primary users, not only the primary base station needs to use the wiretap coding, but also the femtocell base station needs to help to maintain the secrecy transmission for the primary system.
We analyze the achievable secrecy rate with weak secrecy of the cognitive user in the cognitive radio network under the secure coexistence conditions. In addition, we derive the rate constraints to guarantee that the primary user’s weak secrecy is unchanged as well, which requires different analysis compared to , , . For example, the relation between channels observed by the primary transmitter before and after the cognitive transmitter is active should investigated for proper relay and jamming design. Otherwise, either the reliability of the cognitive user or the secrecy of the primary user will be violated. In Fig. 1 we show two improper system designs, where the black rectangular denotes the wiretap code used by the primary user, i.e., the row and column of it are indexed by the secure and confusion messages, respectively and each entry is a codeword. The height and width of the blue rectangular denote the capacity of the channels between the primary transmitter to the primary receiver and that between the primary transmitter to the CR receiver, respectively, after CR transmitter starts to transmit. Fig. 1 (a) shows that, both reliability and secrecy are fulfilled. However, the cognitive transmitter may overdesign the relay power for the primary user’s signal such that the capacity is too large, which is inefficient for the CR user. In particular, that means CR transmitter wastes power on constructing a too good channel for the primary user., while the remained power for CR’s own transmission is reduced. In contrast, Fig. 1 (b) shows that, the relay is efficient, i.e., the new channel is efficient for the transmission of the secure message. However, the confusion rate is not high enough for the new channel, which causes that the secrecy is violated. Therefore, the analysis of the aforementioned rate constraints is important. In addition, we also derive a capacity upper bound for the CR user under both discrete memoryless and additive white Gaussian noise (AWGN) channels to evaluate the performance of the achievable scheme.
We then propose a multi-phase transmission scheme, which considers the following additional phases. First, to accommodate the operations of practical systems, we take into account the first additional phase for listening to/decoding the primary’s signal at the CR transmitter. Note that the primary user’s signal is commonly assumed non-causally known at CR transmitter. Second, we introduce another additional phase as the third one to endow the cognitive system an extra degree of freedom for utilizing different transmission schemes. For AWGN channels, this degree of freedom improves the performance by exploiting pure relaying and jamming but not simultaneously transmitting cognitive user’s own signal.
Finally, we illustrate our results through one numerical example as shown in Fig. 2 based on a geometrical setup, which highlights the impact of the node geometry on the achievable rates and on the optimal power allocation and time splitting of the CR transmitter. Note that we fix the locations of the primary transmitter and receiver at the coordinates (0,0) and (1,0), respectively. The CR receiver is fixed at (1,-1). We assume a path-loss model with path-loss exponent. The power constraints at the primary and CR transmitters are 10 dB and 20 dB, respectively. Note that we also include the power control as a possible design parameter for the CR transmitter, i.e., the transmission power utilized is not necessarily fixed to its maximum. The unit of rate results is bit per channel use. Further numerical results in  show that 1) the proposed 3-phase clean relaying scheme indeed improves the cognitive user’s rate; 2) the proposed achievable scheme is close to capacity when the CR transmitter/receiver is far/close enough to the primary receiver/transmitter, respectively.
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