Two-Way Training for Discriminatory Channel Estimation in Wireless MIMO Systems

This work examines the use of two-way training to efficiently discriminate the channel estimation performances at a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. This work improves upon the original discriminatory channel estimation (DCE) scheme proposed by Chang et al where multiple stages of feedback and retraining were used. While most studies on physical layer secrecy are under the information-theoretic framework and focus directly on the data transmission phase, studies on DCE focus on the training phase and aim to provide a practical signal processing technique to discriminate between the channel estimation performances at LR and UR. A key feature of DCE designs is the insertion of artificial noise (AN) in the training signal to degrade the channel estimation performance at UR. To do so, AN must be placed in a carefully chosen subspace based on the transmitter's knowledge of LR's channel in order to minimize its effect on LR. In this paper, we adopt the idea of two-way training that allows both the transmitter and LR to send training signals to facilitate channel estimation at both ends. Both reciprocal and non-reciprocal channels are considered and a two-way DCE scheme is proposed for each scenario. {For mathematical tractability, we assume that all terminals employ the linear minimum mean square error criterion for channel estimation. Based on the mean square error (MSE) of the channel estimates at all terminals,} we formulate and solve an optimization problem where the optimal power allocation between the training signal and AN is found by minimizing the MSE of LR's channel estimate subject to a constraint on the MSE achievable at UR. Numerical results show that the proposed DCE schemes can effectively discriminate between the channel estimation and hence the data detection performances at LR and UR.Comment: 1

Two-way training for discriminatory channel estimation in wireless MIMO systems

This work examines the use of two-way training to efficiently discriminate the channel estimation performances at a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. This work improves upon the original discriminatory channel estimation (DCE) scheme proposed by Chang where multiple stages of feedback and retraining were used. While most studies on physical layer secrecy are under the information-theoretic framework and focus directly on the data transmission phase, studies on DCE focus on the training phase and aim to provide a practical signal processing technique to discriminate between the channel estimation performances (and, thus, the effective received signal qualities) at LR and UR. A key feature of DCE designs is the insertion of artificial noise (AN) in the training signal to degrade the channel estimation performance at UR. To do so, AN must be placed in a carefully chosen subspace, based on the transmitter's knowledge of LR's channel, in order to minimize its effect on LR. In this paper, we adopt the idea of two-way training that allows both the transmitter and LR to send training signals to facilitate channel estimation at both ends. Both reciprocal and nonreciprocal channels are considered and a two-way DCE scheme is proposed for each scenario. For mathematical tractability, we assume that all terminals employ the linear minimum mean square error criterion for channel estimation. Based on the mean square error (MSE) of the channel estimates at all terminals, we formulate and solve an optimization problem where the optimal power allocation between the training signal and AN is found by minimizing the MSE of LR's channel estimate subject to a constraint on the MSE achievable at UR. Numerical results show that the proposed DCE schemes can effectively discriminate between the channel estimation and, hence, the data detection performances at LR and UR.This work was supported in part by the National Science Council, Taiwan, by Grant NSC 100-2628-E-007-025-MY3 and Grant NSC 101-2218-E-011-043, and in part by the Australian Research Council's Discovery Projects Funding Scheme (Project no.DP110102548)

A Semiblind Two-Way Training Method for Discriminatory Channel Estimation in MIMO Systems

Discriminatory channel estimation (DCE) is a recently developed strategy to enlarge the performance difference between a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. Specifically, it makes use of properly designed training signals to degrade channel estimation at the UR which in turn limits the UR's eavesdropping capability during data transmission. In this paper, we propose a new two-way training scheme for DCE through exploiting a whitening-rotation (WR) based semiblind method. To characterize the performance of DCE, a closed-form expression of the normalized mean squared error (NMSE) of the channel estimation is derived for both the LR and the UR. Furthermore, the developed analytical results on NMSE are utilized to perform optimal power allocation between the training signal and artificial noise (AN). The advantages of our proposed DCE scheme are two folds: 1) compared to the existing DCE scheme based on the linear minimum mean square error (LMMSE) channel estimator, the proposed scheme adopts a semiblind approach and achieves better DCE performance; 2) the proposed scheme is robust against active eavesdropping with the pilot contamination attack, whereas the existing scheme fails under such an attack.Comment: accepted for publication in IEEE Transactions on Communication

Antenna grouping for general discriminatory channel estimation

Discriminatory channel estimation emerges as a promising method of not only increasing the secrecy rates in conventional wiretap channels, but also providing a valuable tool for solving the authentication problem. In this paper, we revisit the discriminatory channel estimation method by Chang et al. and propose a generalization to the challenging scenario in which the number of antennas at the legitimate receiver equals or exceeds those of the transmitter. The proposed method is based on the simple idea of dividing the receiver antennas into smaller groups. However, the direct application of previous approaches would result into security problems due to the multiple observations of the eavesdropper, and therefore the transmission system needs to be designed taking this fact into account. The performance of the proposed technique is illustrated by means of some numerical examples, which clearly show the feasibility of discriminatory channel estimation even in the case of systems with more antennas at the receiver side.This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R)

On the relaxed maximum-likelihood blind MIMO channel estimation for orthogonal space-time block codes

This paper concerns the maximum-likelihood channel estimation for MIMO systems with orthogonal space-time block codes when the finite alphabet constraint of the signal constellation is relaxed. We study the channel coefficients estimation subspace generated by this method. We provide an algebraic characterisation of this subspace which turns the optimization problem into a purely algebraic one and more importantly, leads to several interesting analytical proofs. We prove that with probability one, the dimension of the estimation subspace for the channel coefficients is deterministic and it decreases by increasing the number of receive antennas up to a certain critical number of receive antennas, after which the dimension remains constant. In fact, we show that beyond this critical number of receive antennas, the estimation subspace for the channel coefficients is isometric to a fixed deterministic invariant space which can be easily computed for every specific OSTB code

Capacity-Achieving Iterative LMMSE Detection for MIMO-NOMA Systems

This paper considers a iterative Linear Minimum Mean Square Error (LMMSE) detection for the uplink Multiuser Multiple-Input and Multiple-Output (MU-MIMO) systems with Non-Orthogonal Multiple Access (NOMA). The iterative LMMSE detection greatly reduces the system computational complexity by departing the overall processing into many low-complexity distributed calculations. However, it is generally considered to be sub-optimal and achieves relatively poor performance. In this paper, we firstly present the matching conditions and area theorems for the iterative detection of the MIMO-NOMA systems. Based on the proposed matching conditions and area theorems, the achievable rate region of the iterative LMMSE detection is analysed. We prove that by properly design the iterative LMMSE detection, it can achieve (i) the optimal sum capacity of MU-MIMO systems, (ii) all the maximal extreme points in the capacity region of MU-MIMO system, and (iii) the whole capacity region of two-user MIMO systems.Comment: 6pages, 5 figures, accepted by IEEE ICC 2016, 23-27 May 2016, Kuala Lumpur, Malaysi