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

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 results presented.

### **5.1. Power reduction strategy**

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

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 SNR.

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

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 estimated channel **Hˆ** is usually modeled as

$$\mathbf{H} = \mathbf{\hat{H}} + \mathbf{E} \tag{19}$$

where the matrix **<sup>E</sup>** represents the channel estimation error, and it is independent from **Hˆ** . The knowledge of **Hˆ** is used by the transmitter to obtain the RCI precoding matrix. The entries of **Hˆ** and **<sup>E</sup>** are i.i.d. complex Gaussian random variables with zero mean and variances 1 − *τ*<sup>2</sup> and *τ*2, respectively. The value of *τ* ∈ [0, 1] depends on the quality and technique used for channel estimation. When *τ* = 0 the CSI is perfectly known, whereas *τ* = 1 corresponds to the case when no CSI is available at all.

Future research could analyze the performance of linear precoding in the presence of imperfect CSI, deriving the achievable secrecy sum-rate as a function of the channel estimation error variance *τ*2. This would allow to study how the CSI estimation error must scale with the SNR, in order to maintain a given high-SNR rate gap to the case with perfect CSI, so that the multiplexing gain is not affected. More specifically, the case of frequency division duplex (FDD) systems could be studied. Assuming that users quantize their channel directions by using *B* bits and employing random vector quantization (RVQ), and that they feed the quantization index back to the transmitter [30, 31], it would be interesting to determine how many feedback bits are required by each user in order to maintain a constant gap to the case with perfect CSI.
