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Canadian Workshop on Information Theory (CWIT)

The operational secrecy capacity of cognitive radio MIMO channel

Limeng Dong, Sergey L. Loyka, Y. Li

Published Jun 1, 2017• 4 citations
Publisher

Abstract

Secure communications over cognitive radio (CR) MIMO channels is studied. The secrecy capacity, defined operationally as the maximum achievable secrecy rate subject to reliability and secrecy constraints, of CR MIMO wiretap channel is established under power and interference constraints, including a number of closed-form expressions, bounds and related properties. The secrecy capacity of this channel can be expressed as a minimax game between the transmitter (who selects the input covariance) and nature (who selects the noise covariance). Neither player can deviate from an optimal strategy without incurring a penalty.

DOI
10.1109/cwit.2017.7994824

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Secure communications over cognitive radio (CR) MIMO channels is studied. The secrecy capacity, defined operationally as the maximum achievable secrecy rate subject to reliability and secrecy constraints, of CR MIMO wiretap channel is established under power and interference constraints, including a number of closed-form expressions, bounds and related properties. The secrecy capacity of this channel can be expressed as a minimax game between the transmitter (who selects the input covariance) and nature (who selects the noise covariance). Neither player can deviate from an optimal strategy without incurring a penalty.
This paper studies the achievable rates of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channel with multiple single-/multi-antenna eavesdroppers. By assuming Gaussian input, the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by existing methods. To handle this difficulty, this paper explores a new relationship between the secrecy channel and the recently developed cognitive radio (CR) channel, in which the secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called "interference temperature (IT)" constraints. By constructing an auxiliary multi-antenna CR channel that has the same channel responses as the secrecy channel, this paper shows that the optimal transmit covariance to achieve the maximum secrecy rate is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Thereby, finding the optimal complex transmit covariance matrix for the secrecy channel becomes equivalent to searching over a set of real IT constraints in the auxiliary CR channel. Based on this relationship, efficient algorithms are proposed to solve the non-convex secrecy rate maximization problem by transforming it into a sequence of convex CR spectrum sharing capacity computation problems, under various setups of the secrecy channel.
This paper studies the capacity of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channels with multiple eavesdroppers having single/multiple antennas. It is known that the MIMO secrecy capacity is achievable with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The MIMO secrecy capacity computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by standard convex optimization techniques. To handle this difficulty, we explore a relationship between the MIMO secrecy channel and the recently developed MIMO cognitive radio (CR) channel, in which the multi-antenna secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called ``interference temperature (IT)'' constraints. By constructing an auxiliary CR MIMO channel that has the same channel responses as the MIMO secrecy channel, we prove that the optimal transmit covariance matrix to achieve the secrecy capacity is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Based on this relationship, several algorithms are proposed to solve the non-convex secrecy capacity computation problem by transforming it into a sequence of CR spectrum sharing capacity computation problems that are convex. For the case with single-antenna eavesdroppers, the proposed algorithms obtain the exact capacity of the MIMO secrecy channel, while for the case with multi-antenna eavesdroppers, the proposed algorithms obtain both upper and lower bounds on the MIMO secrecy capacity.
This paper studies the achievable rates of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channel with multiple single-/multi-antenna eavesdroppers. It is known that the maximum achievable secrecy rate is obtained with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The maximum secrecy rate computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by existing methods. To handle this difficulty, this paper explores a new relationship between the secrecy channel and the recently developed cognitive radio (CR) channel, in which the secondary user transmits over the same spectrum simultaneously with multiple primary users, subject to the received interference power constraints at the primary users, or the so-called ¿interference temperature (IT)¿ constraints. By constructing an auxiliary multi-antenna CR channel that has the same channel responses as the secrecy channel, this paper shows that the optimal transmit covariance to achieve the maximum secrecy rate is the same as that to achieve the CR spectrum sharing capacity with properly selected IT constraints. Thereby, finding the optimal complex transmit covariance matrix for the secrecy channel becomes equivalent to searching over a set of real IT constraints in the auxiliary CR channel. Based on this relationship, efficient algorithms are proposed to solve the non-convex secrecy rate maximization problem by transforming it into a sequence of convex CR spectrum sharing capacity computation problems, under various setups of the secrecy channel.
Secure signaling over multiple-input multiple-output (MIMO) channels (WTC) in cognitive radio (CR) systems is studied using the CR MIMO WTC model supplemented with the interference power constraint so that interference to the primary receiver (PR) does not exceed a threshold while ensuring simultaneously no information leakage to an eavesdropper. Based on the recent secrecy capacity results, a number of closed-form analytical solutions for optimal secure signalling (transmit covariance matrix) are established, along with related properties and bounds. This complements known results for the single-antenna (MISO) case as well as numerical algorithms developed in the literature for the general case.
The multiple-input multiple-output (MIMO) Gaussian wire-tap channel (WTC) model is considered in the cognitive radio (CR) setting, where there is a interference power constraint (IPC), in addition to the total transmit power constraint (TPC). Based on the recently established mini-max characterization of its secrecy capacity, a numerical algorithm for global maximization of secrecy rates over such channels is proposed, which is based on the barrier method in combination with the residual-form Newton method and backtracking line search. Unlike the known algorithms, the proposed algorithm is guaranteed to converge to a global (rather than local) optimum. Its efficient performance is illustrated by examples.
We consider the multiple-input multiple-output (MIMO) wiretap channel under a minimum receiver-side power constraint in addition to the usual maximum transmitter-side power constraint. This problem is motivated by energy harvesting communications with wireless energy transfer, where an added goal is to deliver a minimum amount of energy to a receiver in addition to delivering secure data to another receiver. In this paper, we characterize the exact secrecy capacity of the MIMO wiretap channel under transmitter and receiver-side power constraints. We first show that solving this problem is equivalent to solving the secrecy capacity of the wiretap channel under a double-sided correlation matrix constraint on the channel input. We show the converse by extending the channel enhancement technique to our case. We present two achievable schemes that achieve the secrecy capacity: the first achievable scheme uses a Gaussian codebook with a fixed mean, and the second achievable scheme uses artificial noise (or cooperative jamming) together with a Gaussian codebook. The role of the mean or the artificial noise is to enable energy transfer without sacrificing from the secure rate. This is the first instance of a channel model where either the use of a mean signal or the use of channel prefixing via artificial noise is strictly necessary for the MIMO wiretap channel. We then extend our work to consider a maximum receiver-side power constraint instead of a minimum receiver-side power constraint. This problem is motivated by cognitive radio applications, where an added goal is to decrease the received signal energy (interference temperature) at a receiver. We further extend our results to: requiring receiver-side power constraints at both receivers; considering secrecy constraints at both receivers to study broadcast channels with confidential messages; and removing the secrecy constraints to study the classical broadcast channel.