Physical layer security for multi-user MIMO systems

Abstract

This thesis studies physical layer security for multi-user multiple-input multiple-output (MIMO) wireless systems. Due to the broadcast nature of the physical medium, wireless multi-user communications are very susceptible to eavesdropping, and it is critical to protect the transmitted information. Security of wireless communications has traditionally been achieved at the network layer with cryptographic schemes. However, classical cryptography might not be suitable in large dynamic networks, since it requires key distribution and management, and complex encryption/decryption algorithms. A method that exploits the characteristics of wireless channels, known as physical layer security, was proposed as an alternative to achieve perfect secrecy without requiring encryption keys. The rates at which messages can be reliably transmitted to an intended user while no information is leaked at the eavesdroppers, denoted as the secrecy rates, have been studied for several network topologies. However, the secrecy rates achievable in generic multi-user networks are still unknown. Hence in this thesis we study the secrecy rates achievable in multi-user systems with practical transmission schemes.

We propose a linear precoder based on regularized channel inversion (RCI) for the broadcast channel with confidential messages (BCC). In the BCC, a multi-antenna base station (BS) simultaneously transmits independent confidential messages to several spatially dispersed malicious users that can eavesdrop on each other. We carry out a large-system analysis and obtain closed form expressions for the achievable secrecy rates under Rayleigh fading, as well as the optimal regularization parameter and the optimal network load. Simulations confirm that our analysis is accurate even for finite systems. We compare the secrecy rate of the proposed precoder to two upper bounds obtained without secrecy requirements and without interference, respectively, and show that it has the same scaling factor as the two bounds in the high signal-to-noise ratio (SNR) regime. We further extend our analysis to more practical scenarios where only imperfect channel state information is available at the BS, and where channel correlation is present among the transmit antenna elements.

We then introduce the broadcast channel with confidential messages and external eavesdroppers (BCCE). Unlike the BCC, in the BCCE not just malicious users, but also randomly located external nodes can act as eavesdroppers. We obtain the probability of secrecy outage and the mean secrecy rate for the RCI precoder in the BCCE, for the two cases of non-colluding and colluding eavesdroppers. We show that, irrespective of the collusion strategy at the external eavesdroppers, a large number of transmit antennas drives both the probability of secrecy outage and the rate loss due to the presence of external eavesdroppers to zero. Increasing the density of eavesdroppers by a factor $n$, requires $n^2$ as many antennas to meet a given probability of secrecy outage and a given mean secrecy rate. Our analysis demonstrates that the number of transmit antennas at the BS is a key resource to secure communications against malicious users and external eavesdropping nodes.

We finally turn our attention to cellular networks where, unlike the case of isolated cells, multiple BSs generate inter-cell interference, and malicious users of neighboring cells can cooperate to eavesdrop. We characterize the probability of secrecy outage and the mean secrecy rate with RCI precoding, accounting for the spatial distribution of BSs and users and the fluctuations of their channels. We find that RCI precoding can achieve a non-zero secrecy rate with probability of outage smaller than one. However we also find that unlike isolated cells, the secrecy rate in a cellular network does not grow monotonically with the SNR, and the network tends to be in secrecy outage if the transmit power grows unbounded. We further show that there is an optimal value for the density of BSs that maximizes the secrecy rate, and this value is a decreasing function of the SNR. Using the developed analysis, we clearly establish the importance of designing the transmit power and the BS deployment density to make communications robust against malicious users in other cells.