Secured Communication over Frequency-Selective Fading Channels: a practical Vandermonde precoding

In this paper, we study the frequency-selective broadcast channel with confidential messages (BCC) in which the transmitter sends a confidential message to receiver 1 and a common message to receivers 1 and 2. In the case of a block transmission of N symbols followed by a guard interval of L symbols, the frequency-selective channel can be modeled as a N * (N+L) Toeplitz matrix. For this special type of multiple-input multiple-output (MIMO) channels, we propose a practical Vandermonde precoding that consists of projecting the confidential messages in the null space of the channel seen by receiver 2 while superposing the common message. For this scheme, we provide the achievable rate region, i.e. the rate-tuple of the common and confidential messages, and characterize the optimal covariance inputs for some special cases of interest. It is proved that the proposed scheme achieves the optimal degree of freedom (d.o.f) region. More specifically, it enables to send l <= L confidential messages and N-l common messages simultaneously over a block of N+L symbols. Interestingly, the proposed scheme can be applied to secured multiuser scenarios such as the K+1-user frequency-selective BCC with K confidential messages and the two-user frequency-selective BCC with two confidential messages. For each scenario, we provide the achievable secrecy degree of freedom (s.d.o.f.) region of the corresponding frequency-selective BCC and prove the optimality of the Vandermonde precoding. One of the appealing features of the proposed scheme is that it does not require any specific secrecy encoding technique but can be applied on top of any existing powerful encoding schemes.Comment: To appear in EURASIP journal on Wireless Communications and Networking, special issue on Wireless Physical Security, 200

Pilot contamination attacks in massive MIMO systems

© 2017 IEEE. We consider a single-cell massive multiple-input multiple-output (MIMO) system in which a base station (BS) with a large number of antennas simultaneously transmits to K single-antenna users in the presence of an attacker. Massive MIMO systems often operate in a time division duplexing (TDD) fashion. The BS estimates the channel state information (CSI) at receivers based on their uplink pilot transmissions. Downlink transmission rates are highly dependent on these estimates, as the BS utilizes the CSI to exploit the beamforming gain offered by massive MIMO. However, this CSI estimation phase is vulnerable to malicious attacks. Specifically, an attacker can contaminate the uplink pilot sequences by generating identical pilot signals to those of legitimate users. We formulate a denial of service (DoS) attack in which the attacker aims to minimize the sum-rate of downlink transmissions by contaminating the uplink pilots. We also consider another attack model where the attacker generates jamming signals in both the CSI estimation and data transmission phases by exploiting in-band full-duplex techniques. We study these attacks under two power allocation strategies for downlink transmissions. Our analysis is conducted when the attacker knows or does not know the locations of the BS and users. When the attacker does not have perfect location information, stochastic optimization techniques are utilized to assess the impact of the attack. The formulated problems are solved using interior-point, Lagrangian minimization, and game-theoretic methods. We obtain a closed-form solution for a special case of the problem. Our results indicate that even though the attacker does not have the perfect location information, proposed pilot contamination attacks degrade the throughput of a massive MIMO system by more than 50%, and reduce fairness among users significantly. In addition, we show that increasing the number of pilot symbols does not prevent the proposed attacks, if the BS uniformly allocates powers for downlink transmissions

Fundamental bound on the persistence and capacity of short-term memory stored as graded persistent activity

It is widely believed that persistent neural activity underlies short-term memory. Yet, as we show, the degradation of information stored directly in such networks behaves differently from human short-term memory performance. We build a more general framework where memory is viewed as a problem of passing information through noisy channels whose degradation characteristics resemble those of persistent activity networks. If the brain first encoded the information appropriately before passing the information into such networks, the information can be stored substantially more faithfully. Within this framework, we derive a fundamental lower-bound on recall precision, which declines with storage duration and number of stored items. We show that human performance, though inconsistent with models involving direct (uncoded) storage in persistent activity networks, can be well-fit by the theoretical bound. This finding is consistent with the view that if the brain stores information in patterns of persistent activity, it might use codes that minimize the effects of noise, motivating the search for such codes in the brain

Fundamental bound on the persistence and capacity of short-term memory stored as graded persistent activity

It is widely believed that persistent neural activity underlies short-term memory. Yet, as we show, the degradation of information stored directly in such networks behaves differently from human short-term memory performance. We build a more general framework where memory is viewed as a problem of passing information through noisy channels whose degradation characteristics resemble those of persistent activity networks. If the brain first encoded the information appropriately before passing the information into such networks, the information can be stored substantially more faithfully. Within this framework, we derive a fundamental lower-bound on recall precision, which declines with storage duration and number of stored items. We show that human performance, though inconsistent with models involving direct (uncoded) storage in persistent activity networks, can be well-fit by the theoretical bound. This finding is consistent with the view that if the brain stores information in patterns of persistent activity, it might use codes that minimize the effects of noise, motivating the search for such codes in the brain