Preventing Eavesdropper by Artificial Noise in MIMO-OFDM Systems

Abstract

The PHY security has been the focus of the researchers since the day it was proposed. The researchers have mentioned many kinds of methods to prevent the eavesdropper from overhearing the confidential signal in different types of networks and environments. However, none of them have proposed a method which can be used in MIMO-OFDM. In this paper, we propose a new method to protect the confidential signal from the eavesdropper. We present a new antennas allocation scheme to make a full use of the CSI of the transmitter and helpers, and propose a double check scheme to distinguish the eavesdropper from helpers. At last, we use GA solve the optimization equation and gain the maximum of the secrecy capacity within limited power consumption. To the best of our knowledge, this is the first method of dealing with the eavesdropper in MIMO-OFDM, and both the schemes, including the antennas allocation scheme and the double check scheme, are the first of its kinds in this type of network environment.

Appendix: Solution of \({\mathbf {v}}_i\)

From Eq. (17), we can simplify the equation by decompose ${\mathbf {v}}_i$ as ${\mathbf {v}}_i={\mathbf {Bz}}$, where ${\mathbf {B}}$ satisfies the equation

$$\begin{aligned} {\mathbf {B}}=\left( {\mathbf {E}}-\frac{{\mathbf {D}}^{\dag }_{hri}{\mathbf {D}}_{hri}}{\parallel {{\mathbf {D}}_{hri}}\parallel ^2_F}\right) ,\quad i=1,2,\ldots ,N. \end{aligned}$$

(36)

One can note that ${\mathbf {B}}$ is a Hermitian matrix and ${\mathbf {BB}}={\mathbf {B}}$. Then ${\mathbf {B}}$ is a symmetric idempotent matrix. The optimization is equivalent to the following form,

$$\begin{aligned} \max _{\mathbf {Bz}}{\sum _{N}\mid {{\mathbf {D}}^{\dag }_{he}\mathbf {Bz}}\mid {^2}}. \end{aligned}$$

(37)

To simplify the expression, we extract one CSI matrix as example. ${\mathbf {z}}$ shall be in the same direction of the diagonal vector of $({\mathbf {D}}^{\dag }_{hei}{\mathbf {B}})^\dag$, where $i=1,2,\ldots ,N$. So we can get the following equation,

$$\begin{aligned} {\mathbf {v}}_i=\mathbf {Bz}={\mathbf {B}}\frac{diagV({\mathbf {B}}^\dag {\mathbf {D}}_{hei})}{\parallel {{\mathbf {D}}^{\dag }_{hei}{\mathbf {B}}}\parallel ^2_F},\quad i=1,2,\ldots ,N. \end{aligned}$$

(38)

Here, we propose a Lemma to deduce the equation one step further.

Lemma 1

To a diagonal matrix ${\mathbf {B}}$ and any non-zero matrix $\mathbf {C}$,

$$\begin{aligned} {\mathbf {B}}diagV(\mathbf {C})=diagV(\mathbf {BC}). \end{aligned}$$

(39)

According to the Lemma 1, Eq. (38) can be simplified as

$$\begin{aligned} {\mathbf {v}}_i=\frac{{\mathbf {B}}diagV({\mathbf {D}}_{hei})}{\parallel {{\mathbf {D}}^{\dag }_{hei} {\mathbf {B}}}\parallel ^2_F}, i=1,2,\ldots ,N. \end{aligned}$$

(40)

Plugging ${\mathbf {B}}$ into Eq. (40), we can get Eq. (17).