**6. Conclusions**

12 Recent Trends in Multiuser MIMO Communications

0

the MISOME channel (circles) are also plotted.

**5.1. Power reduction strategy**

estimated channel **Hˆ** is usually modeled as

results presented.

SNR.

1

2

Per-user

3

 secrecy rate

4

5

6

Cs,SU

RCI-PA RCI-EP

RCI-EP (no secrecy)

0 5 10 15 20 25

ρ [dB]

**Figure 5.** Per-user secrecy rate vs. *ρ* for *β* = 1 and *K* = 4 users: with equal power allocation (solid) and with optimal power allocation (dashed). The rate of the optimal RCI precoder without secrecy requirements (squares) and the secrecy capacity of

Before concluding this chapter, we briefly discuss current research topics on physical layer security for multiuser MIMO communications, and we mention possible extensions of the

Since for *β* > 1 the RCI precoder performs poorly in the high-SNR regime, a linear precoder based on RCI and power reduction could significantly increase the high-SNR secrecy sum-rate. In fact, we can observe from Fig. 2 that when *β* > 1 there is an optimal

A power reduction strategy would prevent the secrecy sum-rate from decreasing at high SNR by reducing the transmit power, and therefore reducing the SNR to the value that maximizes the secrecy sum-rate. For 1 < *β* < 2 and large SNR, the RCI precoder with power reduction would thus achieve a constant nonnegative secrecy sum-rate. However, this strategy would not be effective for *β* ≥ 2, since in this case the secrecy sum-rate is zero irrespective of the

In Sections 3 and 4, we discussed the secrecy rate performance of multi-user MIMO linear precoding for the case when perfect channel state information (CSI) is available at the transmitter. However, a more realistic scenario is the one where only an estimation of the channel is available at the transmitter. The relation between the true channel **H** and the

*<sup>s</sup>* starts decreasing.

**5. Current research on multiuser MIMO physical layer security**

value of the SNR beyond which the achievable secrecy sum-rate *<sup>R</sup>*⋆◦

**5.2. Secrecy sum-rates in the presence of channel estimation error**

Throughout this chapter, we presented an up-to-date summary of the research in the field of physical layer security for multiuser MIMO communications. Unlike classical cryptography, physical layer security does not require key distribution and management, it does not rely on the limited computational power of the eavesdroppers, and it does not employ complex encryption algorithms. For these reasons, it is suitable for large dynamic wireless networks, and it has been proposed to enhance the protection of confidential messages transmitted over wireless channels. In this chapter, we especially focused on the problem of secret communication in a multiuser MIMO system. We considered the general case where a multiantenna base station transmits independent confidential messages to a generic number of users. We assumed that the users can potentially act maliciously and eavesdrop on each other. For this system set-up, we presented some transmission schemes based on linear precoding. We discussed the performance of these schemes as well as the cost of simultaneously guaranteeing secrecy to multiple users.

It has been recently shown that, in the large SNR regime, a linear precoding scheme based on regularized channel inversion can achieve secrecy without reducing the sum-rate at no additional cost when the number of transmit antennas *M* is larger than the number of users *K*. If *K* = *M*, secrecy can be achieved with a small rate loss or, alternatively, without reducing the sum-rate at a cost of less than 4dB in terms of the power transmitted. However, the secrecy requirements limit the maximum number of users that can be served with a non-zero rate. When *K* > *M*, there is an optimal value of the SNR beyond which the achievable rate starts decreasing, and at large SNR the secrecy sum-rate achievable by RCI precoding is poor. The base station could prevent the secrecy sum-rate from decreasing by reducing the transmit power, and therefore the SNR, to the value that maximizes the secrecy sum-rate. This would result in a constant nonnegative high-SNR secrecy sum-rate. However, this strategy would not be effective if *K* ≥ 2*M*.

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