**2. Physical layer security in multiuser MIMO systems**

One way to extend the concept of physical layer security to multiuser systems is by considering the multiuser wiretap channel, where a transmitter wants to have confidential communication with an arbitrary number of trusted users in the presence of an external eavesdropper. For this system set-up, the secrecy capacity region in the presence of an arbitrary number of legitimate receivers was characterized in [14], by using the relationship between the minimum-mean-square-error and the mutual information. The capacity achieving coding scheme was shown to be a variant of dirty-paper coding with Gaussian signals.

Since the transmitter cannot always predict the behavior of the users, the multiuser MIMO channel with malicious users is now regarded with large interest. This is also denoted as the broadcast channel with confidential messages (BCC). Consider a broadcast channel with two independent confidential messages sent to two receivers, where each receiver acts as an eavesdropper for the other one. In other words, the first message is intended for the first receiver but needs to be kept secret from the second receiver, and viceversa. This scenario was studied in [15] for the multiple-input single-output (MISO) Gaussian case and in [16] for general MIMO Gaussian case. In this case it was shown that both confidential messages can be simultaneously transmitted at their respective maximum secrecy rates, and the achievability was obtained using the dirty-paper coding.

2 Recent Trends in Multiuser MIMO Communications

version of the wiretap channel [5].

the intended receiver [11–13].

signals.

user while the rate of information leakage to the eavesdropper vanishes asymptotically with the code length. For the case when the eavesdropper's channel is a degraded version of the intended user's channel, Wyner showed that it is possible to have secret communication without using an encryption key. This can be achieved by a randomized coding scheme where the information is hidden in the additional noise seen by the eavesdropper. Each message is mapped to many codewords, thus inducing maximal equivocation at the eavesdropper. Csizar and Korner generalized Wyner's work by considering a nondegraded

Physical layer security was then applied to Gaussian channels [6], and it was observed that a secret transmission can be achieved only if the channel at the eavesdropper is noisier than the channel at the intended user. The presence of slow fading was shown to significantly change the situation, since it allows the transmitter to employ a variable-rate transmission, thus achieving secrecy even when the eavesdropper's channel is better than the intended receiver's channel on average [7]. Also the use of multiple antennas can enhance the secrecy capability, because it enables the transmitter to beamform in a direction as orthogonal to the eavesdropper and as close to the intended user as possible [8–10]. Even when the channel at the eavesdropper is unknown by the transmitter, artificial noise can be transmitted to degrade the eavesdropper's channel and thus reduce its signal-to-noise ratio, while being harmless to

More recently, physical layer security has also been extended to multiuser MIMO channels. In this chapter, we will survey the research in the field of physical layer security for multiuser MIMO communications, especially focusing on the case when multiple malicious users are present in the network, and they can eavesdrop on each other. For these complex scenarios, we will present some suboptimal low-complexity transmission schemes, discuss their performance and quantify the sum-rate penalties imposed by the secrecy requirements and by the presence of multiple users. We will discuss the challenges that arise in networks with a large number of malicious receivers, we will identify potential ways to deal with these

One way to extend the concept of physical layer security to multiuser systems is by considering the multiuser wiretap channel, where a transmitter wants to have confidential communication with an arbitrary number of trusted users in the presence of an external eavesdropper. For this system set-up, the secrecy capacity region in the presence of an arbitrary number of legitimate receivers was characterized in [14], by using the relationship between the minimum-mean-square-error and the mutual information. The capacity achieving coding scheme was shown to be a variant of dirty-paper coding with Gaussian

Since the transmitter cannot always predict the behavior of the users, the multiuser MIMO channel with malicious users is now regarded with large interest. This is also denoted as the broadcast channel with confidential messages (BCC). Consider a broadcast channel with two independent confidential messages sent to two receivers, where each receiver acts as an eavesdropper for the other one. In other words, the first message is intended for

challenges, and present an outlook on future directions for research.

**2. Physical layer security in multiuser MIMO systems**

Let us cosider now a larger multiuser network with more than two malicious users. For this network, it is required that the base station (BS) securely transmits each confidential message, ensuring that none of the other unintended users receive any information. Since in general the behavior of the users cannot be determined by the transmitter, a conservative worst-case scenario can be assumed for each user, where all the remaining users can cooperate to jointly eavesdrop. In this case, for each user, the alliance of the cooperating eavesdropper is equivalent to a single multi-antenna eavesdropper.

The MISO BCC with a generic number of malicious receivers was studied in [17, 18], and it consists of a BS with *M* antennas that simultaneously transmit independent confidential messages to *K* spatially dispersed single-antenna users, which can cooperate and eavesdrop on each other. Although determining the secrecy capacity region for the generic MISO BCC is still an open problem, suboptimal transmission schemes have been proposed to achieve high secrecy sum-rates by controlling the amount of crosstalk between the users [19]. These schemes are based on linear precoding, and unlike dirty-paper coding, their low complexity makes them suitable for practical implementation. In the following sections, we present some new results on the secrecy sum-rates achieved by multiuser MIMO linear precoding.
