Secrecy at the Physical Layer in the TWC with a Number of Untrusted AF Relays That Harvest Energy from RF Sources and Operate in Half- Duplex Mode

A System Model of TWC with a Number of Untrusted AF Relays

A cognitive TWC network through untrusted AF relays as in Sharma et al. (2020) is considered. All untrusted relays work as relays as well as eavesdroppers. However, at a time, a particular relay is in the active state, and therefore, only active untrusted relay eavesdrops the information signal. Only one information signal is eavesdropped at a time, while another information signal creates interference at the relay. In a CRN. the considered primary network consists of only primary transmitter (PT) and primary receiver (PR). It is also considered that the PT is at a far distance from both the sources and relays and therefore received interference signal from the PT is negligible at the receiving nodes of the cognitive network.

The complete system model is shown in Figure 12.1. In the network, the SI represents the cognitive source one, S2 represents the cognitive source two, and R, represents the i'^h untrusted AF relay. Both the sources and all the relays transmit the signal satisfying the primary network outage constraint. The communication is completed in two-phases; the first phase is the broadcasting phase, and the second phase is the relaying phase as given in Figure 12.2. All nodes in the cognitive and primary

FIGURE 12.1 System model of TWC of CRN with a number of untrusted AF relays that harvest energy and operate in half-duplex mode.

FIGURE 12.2 Time frame of TWC with energy-harvesting relays.

network use an individual single omnidirectional antenna. In the broadcasting phase, both the sources send the information signal to a selected best relay. In the relaying phase, the relay follows the protocol of AF on received signal and broadcasts the signal toward both the sources using an omnidirectional antenna. As per knowledge of perfect channel state information (CSI) and prior transmitted message, both the sources first detect the self-interferer signal in the received signal and then delete that. After removal of the self-interference signal, both the sources easily decode the message without interference. Power corresponding to harvested energy by the selected relay from the RF signals in the broadcasting phase is used in the relaying phase.

All channels are faded with Rayleigh fading. All channel coefficients are random variables of independent nonidentically distributed type. We assume that the channel coefficient from source one (SI) to relay is h_slRi, and source two (S2) to i"‘ relay is h_sm, from i'^h the relay to source two is h_RiS2, and i'^h relay to SI is h_RiS[, the channel from the S1 to the primary receiver is h_S]PR and source two to the primary receiver is

h_nPR, and the channel from PU-TX to PU-RX is h_PP. The channel gains are indicated by g_x, wherex e (S_lR_j,S₂R_j,R_iS_l,R_iS₂,S_iPR,S₂PR,R_iPR,PP). The mean channel gains of all channels are indicated by Q_t. where x e (S_lR_j,S₂R_j,R_!S_i,R_iS₂,S_lPR,S₂PR, RiPR,PP). All channels have additive w'hite Gaussian noise (AWGN) w'ith mean zero and variance N₀. The probability distribution function (PDF) of channel gain is expressed as:

and the cumulative distribution function (CDF) is expressed as:

Power allocation to the cognitive nodes

Assignment of pow'er to the cognitive nodes is based on the outage probability constraint of the primary network (Tran et al. 2013; Sharma et al. 2020). We assume the sources’ transmit power are equal. The primary network has the outage probability, which is expressed as:

where yf_w = 2^1Kl' and P,, is the transmit pow'er of the PT, R_P is the outage threshold rate of the primary network, P_MS is the estimated power assigned to both sources under outage probability constraint of the primary network, AWGN has pow'er N₀ and Д is the primary network outage constraint. The assigned power to both cognitive sources (P_MS) is evaluated from Eq. (12.3) as:

where Q._SP = Cl_S[PR = &_S2PR- In the relaying phase of communication, only the relay transmits the signals. Thus, the assignment of power to relay is only necessary.

Again, we evaluate the power for the relay in the same manner as in Eq. (12.4). The outage probability is expressed as:

The estimated power for the relay is (Tran et al. 2013; Sharma et al. 2020)

The cognitive nodes have limitation of transmit power due to constraint imposed by primary network. Both the cognitive sources have P_PK as a maximum limit of transmit power, and the selected relay has the harvested power (P_Hi) as the maximum limit of transmit power. The final assigned power to both the cognitive sources is given as (Tran et al. 2013; Sharma et al. 2020)

The final assigned power to the selected relay is (Tran et al. 2013; Sharma et al. 2020)

Secrecy Capacity and Relay Selection

We will consider selection of relay based on maximizing the secrecy capacity, which will be shown by Eq. (12.22). First, we shall find the secrecy capacity and then consider the relay selection. The combined information signals received at the particular i"‘ relay is

where n_Q is the AWGN. The energy harvesting circuit, based on a power-splitting scheme, uses a “0” part of the combined received signals to harvest the energy, and another “(1 - 0)” part of combined signal is used in signal processing (Pan et al. 2015; Kalamkar and Banerjee 2017; Sharma et al. 2020). The term “в e. (0,1)” is the PS factor for harvesting energy. The harvested energy is expressed as

where //(О < г/ < 1) is energy transfer efficiency, and T is the complete communication time. The power, based on harvested energy, is

After removal of harvesting part of the signal, the rest part of the signal is expressed as:

The signal strength is represented in signal-to-noise ratio (SNR). The SNR for each information signal at the relay is expressed as:

where y_SiRl is the SNR for the first information signal one, and y_slRl is the SNR for the second information signal. The selected /"’ relay amplifies the information signals with the amplification factor £,■ The C, is expressed as

The i"' relay broadcasts the information signals. The source two receives the signal, which can be expressed as

The source one receives the signal as

The self-interference is canceled at both the sources. The SNR at both the sources is represented as

where y_RiS2 is the SNR for the information signal one at the S2, and y_RlSl is the SNR for the information signal of S2 at the S1.

Using Shannon channel capacity formula, the channel capacities for both the information signal at both the sources are expressed as

The channel capacities of both the information signal at /"' the untrusted relay are expressed as

Now, the secrecy capacity of both the information signals is defined as (Pan et al. 2015; Kalamkar and Banerjee 2017)

where [jc]⁺ indicates maximum between 0 and x. The global secrecy capacity (Q;f^c) is defined as:

Based on maximum secrecy capacity, a particular relay is selected. The selected relay must follow the selection criteria

A final secrecy capacity through a selected untrusted relay out of multiple untrusted relays is expressed as