Table 2 Definitions for key parameter

\(\mathrm{{diag}}\left( x \right)\)

Stands for a diagonal matrix for a vector x, where each diagonal element corresponds to an element in x

\({x^T}\)

The transposition of x

\({\mathbb {E}}\left[ {.} \right]\)

The expectation

\({f_x}\left( . \right)\)

The PDF of a random variable

\({F_x}\left( . \right)\)

The CDF of a random variable

k!

The factorial operation

\(\Pr \left( . \right)\)

The probability

\(\left| . \right|\)

The absolute operations

\({I_a}\left( . \right)\)

The modified Bessel function of the first kind

\({Q_a}\left( . \right)\)

The Marcum Q-function

\(\Gamma \left( . \right)\)

The gamma function

\(\gamma \left( {.,.} \right)\)

The lower incomplete gamma function

\(s_i^d\)

The transmitted signals to \(D_i\), \((i=1,2)\)

\(s_i^{u}\)

The transmit signals of \(D_i\)

\({{P_{BS}}}\)

The transmit power of BS

\({{P_{D_i}}}\)

The transmit power of \(D_i\)

\({{\eta _i}}\)

The power allocation coefficients with \(\left( {{\eta _1} + {\eta _2} = 1} \right)\)

\(\beta\)

The path loss exponent

\({\tau _1}\)

The additive white Gaussian noises (AWGN) at \(D_1\) with zero mean and variance \(N_0\)

\({\tau _2}\)

The AWGN at \(D_2\) with zero mean and variance \(N_0\)

\({\tau _{bs}}\)

The AWGN at BS

\({\tau _e}\)

The AWGN at E with the same variance \({N_e}\)

\(R_i\)

The target data rate of users \(D_i\)

\(R_{Ei}\)

The secrecy rate of the user \(D_i\)

K

Accuracy-complexity tradeoff parameter

\(d_1\)

The distance from BS-IRS

\(d_2\)

The distance from IRS-\(D_2\)

\(d_{g}\)

The distance from BS-\(D_1\)

\(d_{g_e}\)

The distance from BS-E

\(d_{g_{e1}}\)

The distance from \(D_1\)-E

\(d_{g_{e2}}\)

The distance from \(D_2\)-E

\(h_{1,n}^d\)

The channel coefficient from BS-nth reflecting element

\(h_{1,n}^u\)

The channel coefficient from nth reflecting element-BS

\(h_{2,n}^d\)

The channel coefficient from nth reflecting element-\(D_2\)

\(h_{2,n}^u\)

The channel coefficient from \(D_2\)-nth reflecting element

\(g_d\)

The channel coefficient from BS-\(D_1\)

\(g_u\)

The channel coefficient from \(D_1\)-BS

\(g_e\)

The channel coefficient from BS-E

\(g_{e1}\)

The channel coefficient from \(D_1\)-E

\(g_{e2}\)

The channel coefficient from \(D_2\)-E