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Signal Processing

Optimal signal design for coherent detection of binary signals in Gaussian noise under power and secrecy constraints

Berkan Dülek, Sinan Gezici

Published Apr 13, 2023• 1 citation
Publisher
DOI
10.1016/j.sigpro.2023.109052

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In this paper, we investigate the secrecy rate of finite alphabet communications over multiple-input, multiple-output, multiple-antenna eavesdropper (MIMOME) systems. Traditional precoder designs at the transmitter for achieving secrecy capacity (maximum secrecy rate) for MIMOME systems are developed according to the assumption of Gaussian input signals. Such designs may risk substantial secrecy rate loss when Gaussian inputs are replaced by practical finite alphabet inputs. To address this issue, we propose a linear precoding design to directly maximize the secrecy rate for MIMOME systems under the constraint of finite alphabet input. Exploiting convex optimization and matrix calculus, we present necessary conditions required of the optimal precoding design and develop an iterative algorithm for finding an efficient precoder. With finite alphabet input signals, maximum transmission power no longer corresponds to maximum secrecy rate as in the case of Gaussian input. We further derive closed-form results on the optimal transmission design for maximizing secrecy rate in low signal-to-noise ratio (SNR) region and near-optimal transmission power in a high SNR region.
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This thesis examines the challenges of information-theoretic secret communication that exploits the temporal and spatial variations of the wireless medium to improve secret communication rates. We first examine the secrecy capacity of a system consisting of independent parallel channels with one transmitter, one intended receiver and one eavesdropper. We show that the secrecy capacity of the system is the sum of the secrecy capacities of the individual subchannels. We further derive the optimal power allocation strategy for a system of parallel AWGN channels subject to a total power constraint, and also extend the results to random fading channels with additive Gaussian noise. We then study the achievable secrecy rate with Gaussian random codes for the situation where the channel of the intended receiver is a constant AWGN channel, while the eavesdropper's channel is fast Rayleigh fading with unknown realizations but known statistics to the transmitter. The proposed method with artificial noise and bursting provides ways to achieve positive secrecy rate even when Bob's channel is worse than Eve's channel on average. We also examine the achievable secrecy rate for a multiple antenna system, and the optimal input structure needed to achieve this rate. For the multiple input single output case, an analytical solution is derived. Multiple antenna systems provide extra degrees of freedom to the transmitter so that a beamforming-like approach can be used to provide advantage to the intended receiver against the eavesdropper. Next we derive a secrecy capacity outer bound region for a class of one-sided interference channels. The outer bound is shown to be tight for a class of binary deterministic one-sided interference channels, and can be achieved within one bit for some Gaussian one-sided interference channels.Finally, as Gaussian random codes are impractical, we evaluate achievable secrecy rates with discrete signaling. We observe that with discrete signaling, there exists an optimal power that maximizes the achievable secrecy rate. For the AWGN channel, larger constellation is always better. While for fading channel, the optimal constellation size varies with the power constraint, and discrete signaling can perform better than random Gaussian coding.