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arXiv:1108.2858

Optimal Power Allocation for OFDM-Based Wire-Tap Channels with Arbitrarily Distributed Inputs

Haohao Qin, Yin Jian Sun, Chen, Xiang, Zhao, Ming, Wang, Jing

Published Aug 14, 2011• 0 citations
arXivHTMLPDF

Abstract

In this paper, we investigate power allocation that maximizes the secrecy rate of orthogonal frequency division multiplexing (OFDM) systems under arbitrarily distributed inputs. Considering commonly assumed Gaussian inputs are unrealistic, we focus on secrecy systems with more practical discrete distributed inputs, such as PSK, QAM, etc. While the secrecy rate achieved by Gaussian distributed inputs is concave with respect to the transmit power, we have found and rigorously proved that the secrecy rate is non-concave under any discrete inputs. Hence, traditional convex optimization methods are not applicable any more. To address this non-concave power allocation problem, we propose an efficient algorithm. Its gap from optimality vanishes asymptotically at the rate of $O(1/\sqrt{N})$, and its complexity grows in the order of O(N), where $N$ is the number of sub-carriers. Numerical results are provided to illustrate the efficacy of the proposed algorithm.

DOI
10.48550/arxiv.1108.2858

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In this paper, we investigate power allocation that maximizes the secrecy rate of orthogonal frequency division multiplexing (OFDM) systems under arbitrarily distributed inputs. Considering commonly assumed Gaussian inputs are unrealistic, we focus on secrecy systems with more practical discrete distributed inputs, such as PSK, QAM, etc. While the secrecy rate achieved by Gaussian distributed inputs is concave with respect to the transmit power, we have found and rigorously proved that the secrecy rate is non-concave under any discrete inputs. Hence, traditional convex optimization methods are not applicable any more. To address this non-concave power allocation problem, we propose an efficient algorithm. Its gap from optimality vanishes asymptotically at the rate of O(1/N)O(1/\sqrt{N})O(1/N​), and its complexity grows in the order of O(N), where NNN is the number of sub-carriers. Numerical results are provided to illustrate the efficacy of the proposed algorithm.
Optimal power allocation for orthogonal frequency division multiplexing (OFDM) wiretap channels with Gaussian channel inputs has already been studied in some previous works from an information theoretical viewpoint. However, these results are not sufficient for practical system designs. One reason is that discrete channel inputs, such as quadrature amplitude modulation (QAM) signals, instead of Gaussian channel inputs, are deployed in current practical wireless systems to maintain moderate peak transmission power and receiver complexity. In this paper, we investigate the power allocation and artificial noise design for OFDM wiretap channels with discrete channel inputs. We first prove that the secrecy rate function for discrete channel inputs is nonconcave with respect to the transmission power. To resolve the corresponding nonconvex secrecy rate maximization problem, we develop a low-complexity power allocation algorithm, which yields a duality gap diminishing in the order of O(1/√N), where N is the number of subcarriers of OFDM. We then show that independent frequency-domain artificial noise cannot improve the secrecy rate of single-antenna wiretap channels. Towards this end, we propose a novel time-domain artificial noise design which exploits temporal degrees of freedom provided by the cyclic prefix of OFDM systems to jam the eavesdropper and boost the secrecy rate even with a single antenna at the transmitter. Numerical results are provided to illustrate the performance of the proposed design schemes.
Orthogonal frequency division multiplexing (OFDM) systems have enjoyed widespread adoption as the physical layer standard for high data rate wired and wireless networks, due to their ability to efficiently cope with slowly varying dispersive channels. Therefore in searching for feasible implementations of physical layer security techniques, it is appropriate to analyze how existing information theoretic results can be applied to the OFDM structure This paper considers the information theoretic secrecy rates that are achievable in a wiretap OFDM channel when transmitting quadrature amplitude modulation (QAM) constellation symbols. The loss with respect to the secrecy rates obtained with Gaussian distributed inputs is evaluated for both nite constellation cardinalities and in the asymptotic approximation of arbitrarily high cardinality. Moving from the insight gained with this analysis, we propose bit-loading strategies to efficiently allocate the appropriate number of bits in each subchannel, by considering the twofold objective of minimizing the loss with respect to the Gaussian input secrecy capacity and minimizing the total bit load.
The security issue on the physical layer is of significant challenge yet of paramount importance for 5G communications. In some previous works, transmit power allocation has already been studied for orthogonal frequency division multiplexing (OFDM) secure communication with Gaussian channel inputs for both a single user and multiple users. Faced with peak transmission power constraints, we adopt discrete channel inputs (e.g., equiprobable Quadrature Phase Shift Keying (QPSK) with symmetry) in a practical communication system, instead of Gaussian channel inputs. Finite-alphabet inputs impose a more significant challenge as compared with conventional Gaussian random inputs for the multiuser wiretap OFDM systems. This paper considers the joint resource allocation in frequency-domain artificial noise (AN) assisted multiuser wiretap OFDM channels with discrete channel inputs. This security problem is formulated as nonconvex sum secrecy rate optimization by jointly optimizing the subcarrier allocation, information-bearing power, and AN-bearing power. To this end, with a suboptimal subcarrier allocation scheme, we propose an efficient iterative algorithm to allocate the power between the information and the AN via the Lagrange duality method. Finally, we carry out some numerical simulations to demonstrate the performance of the proposed algorithm.
The security issue on the physical layer is of significant challenge yet paramount importance for 5G communications. In some previous works, transmit power allocation has already been studied for orthogonal frequency division multiplexing (OFDM) secure communication with Gaussian channel inputs for both a single user and multiple users. Facing with peak transmission power constraints, we adopt discrete channel inputs (e.g., QPSK) in practical communication system, instead of Gaussian channel inputs. Discrete channel inputs impose a more significant challenge as compared with conventional Gaussian channel inputs for the multiuser wiretap OFDM system. This paper considers the joint resource allocation for time-domain artificial noise (AN) aided multiuser wiretap orthogonal frequency-division multiplexing (OFDM) channels with discrete channel inputs, providing secure 5G communications. This security problem is formulated as nonconvex sum secrecy rate optimization by jointly optimizing the subcarrier allocation, information-bearing power and AN-bearing power. To this end, with suboptimal subcarrier allocation scheme, we develop an efficient iterative algorithm to allocate the power between the signal and the AN via the Lagrange duality method. Finally, we carry out some numerical simulation to demonstrate the performance of the proposed algorithms.
Orthogonal frequency division multiplexing (OFDM) has been established as the preferred modulation choice for high-rate data transmission over dispersive channels, as it allows rejection of inter-symbol interference (ISI) and efficient utilization of the available spectrum. We address the issues of determining achievable secrecy rates and secrecy capacity for OFDM transmission in the presence of a generic eavesdropper. In doing so, we refrain from making the restrictive assumption made in previous works that the eavesdropper uses a standard fast Fourier transform (FFT)-based demodulator. First, the high SNR secrecy capacity under a total input power constraint is evaluated for both cyclic prefix and zero-padding suffix OFDM systems. It is shown that in both cases the result is sensibly lower than what we would get if the eavesdropper used an OFDM receiver. Then, optimal power allocation schemes are proposed for both types of OFDM systems and the secrecy rates are compared with results obtained by using existing power allocation methods described in the literature for parallel Gaussian wiretap channels and multiple-input multiple-output (MIMO) Gaussian wiretap channels.
In this paper, the resource allocation for multiuser wiretap Orthogonal Frequency-Division Multiplexing(OFDM) systems is investigated to improve the system power efficiency. In such a multiuser wiretap OFDM system, one legitimate transmitter (Alice), multiple legitimate receivers (Bobs), and one eavesdropper (Eve) are simultaneously considered. The time-domain artificial noise (AN) is firstly involved to guarantee the target secrecy rates of multiple Bobs. Different from the traditional sum secrecy rate maximization problem which may result in the unfair transition for Bobs with bad channel gains and more transmit power consumptions, a non-convex transmit power minimization problem is formulated to jointly optimize the power, subcarrier allocation and AN design, in which a target secrecy rate for each individual Bob is ensured. An iterative algorithm is further proposed to solve this power minimization problem by updating the subcarrier, power allocation and AN design alternatively. Numerical simulation results demonstrate the effectiveness of the proposal, including the improvements of system power efficiency and the fairness of multiple Bobs.