Secret key generation (SKG) is an emerging technology to secure wireless communication from attackers. Therefore, the SKG at the physical layer is an alternate solution over traditional cryptographic methods due to wireless channels’ uncertainty. However, the physical layer secret key generation (PHY-SKG) depends on two fundamental parameters, i.e., coherence time and power allocation. The coherence time for PHY-SKG is not applicable to secure wireless channels. This is because coherence time is for a certain period of time. Thus, legitimate users generate the secret keys (SKs) with a shorter key length in size. Hence, an attacker can quickly get information about the SKs. Consequently, the attacker can easily get valuable information from authentic users. Therefore, we considered the scheme of power allocation to enhance the secret key generation rate (SKGR) between legitimate users. Hence, we propose an alternative method, i.e., a power allocation, to improve the SKGR. Our results show 72% higher SKGR in bits/sec by increasing power transmission. In addition, the power transmission is based on two important parameters, i.e., epsilon and power loss factor, as given in power transmission equations. We found out that a higher value of epsilon impacts power transmission and subsequently impacts the SKGR. The SKGR is approximately 40.7% greater at 250 from 50 mW at

Security is profoundly important due to the rapid increase in wireless communication. In 2018, Ericsson announced that 5G subscribers would hit 1.9 billion by the end of 2024. It is also predicted that the networks would hold 35% of data and serve 65% of the global population [

Alternatively, Shannon’s well-known work showed that channel reciprocity among authentic users at the physical layer (PHY) had achieved special consideration [

Keeping the above discussion, the researchers in [

Moreover, in [

Nonetheless, the research indicates that low SKGR is the main limitation for PHY-SKG [

Due to the limited time duration, the authentic users generate shorter length of SKs. Therefore, an attacker can get information about SKs among legitimate users. Conversely, we examine the power allocation strategy to generate SKs. We illustrate a power allocation scheme to investigate SKGR.

Our results show 72% higher SKGR (bits/sec) at higher power allocation than low power allocation. To prove our result, we also analyze other factors, such as epsilon (

The rest of our paper is organized as follows. We illustrate the system model, formulation, and proposed solution in Section 2. The simulation results are discussed in Section 3. Section 4 concludes the paper.

In the system model, two authentic users, i.e., _{1} and _{2} are considered. First, _{1} transmits the signal _{u1}. The receiver _{2}, receives the signal _{u2} = _{1}_{u1} +_{u2}. Here, _{1} represents the channel gain while _{u2} represents the noise factor at _{2}. Likewise, _{2} transmits the signals _{u2} and _{1} receives the signal, i.e., _{u1} = _{2}_{u2} +_{u1}. Here, _{2} represents the gain of channel while _{u1} denotes the noise factor at _{1}. The authentic users, i.e., _{1} and _{2} assume the channel gain _{1} and _{2}, respectively. Furthermore, we assume _{u1} be the transmitted signal by _{1}. Hence, the channel gain at _{2} is

where _{u1}. Similarly, the _{1} is

The fundamental description of SKGR between _{1} and _{2} is described as the mutual information

Since

and

The correlation coefficient between _{u1} and _{u2} is

Therefore, the covariance matrix of

and

The entropy can be calculated by

Substituting

Let

_{1} and _{2}. In a realistic scenario, users send data over several links concurrently by allocating power. From

where _{u1T}, and _{u2T}, are the total powers transmitted by _{1} and _{2}, respectively. Nonetheless, to get the optimal solution, we need the validation of convexity and concavity of our objective functions, as mentioned in _{u1}, and _{u2}, respectively. Furthermore, we also considered Lagrangian form on

and assume the conditions of Karush Kuhn Tucker (KKT) as

It is observed from _{u1T} − _{u1} = 0. It is noted that the transmitter uses power higher than zero, i.e., _{u2}) is initially distributed equally. Therefore, as outlined in Algorithm 1, we can resolve the proposed power allocation strategy in Algorithm 2. The symmetric method of SKG helps us to rewrite the Lagrangian for all steps of the power allocation process in a similar way. From the power allocation of _{1}, the following optimization problem at _{2} is given by

Now, we apply the same approach as discuss for the power allocation of _{1}, and is given by

Algorithm 1 can be updated for the transmitter _{1} based on _{1} is discussed in Algorithm 2.

We figure out the SKGR by considering power allocation and to exploit different parameters in our simulation results. The coherence time is set to _{1} & _{n}_{1} and _{2} is 70 m. Furthermore, the SKGR is 26 bits/s at 20 m between legitimate users by considering 50 mW power. This indicates that more power is needed to produce higher SKs. Nonetheless, when we increase the distance between _{1} and _{2}, the SKGR decreases because of the large distances between legitimate users. This is because when the distance increases, the SNR decreases between _{1} and _{2}, and hence, SKGR decreases. Nonetheless, the result also reveals that the SKGR rises with increasing power, regardless of the distances between _{1} and _{2}. It proves that even though the distance can impact the SKGR because of increased power, the SKGR increases. For illustration, the SKGR is approximately equal to 25–26 bit/s at 250 mW. The results also indicate that the SKGR depends not only on the coherence time but also on the transmission power.

We also analyze the power transmission versus

Finally, by varying the value of

We introduced a mechanism to generate SKs and enhance the SKGR with power allocation. It guarantees the reliability of decentralized wireless networks. From the existing works, it is noticed that the coherence time for SKGR may not always be possible because coherence time produces a small length of SKs. Consequently, the intruders can easily obtain the SKs between authentic users. Therefore, we consider the power allocation scheme to generate SKs and enhance SKGR. Our research has shown that we can get a higher SKGR by increasing the transmitting power. The simulation results showed that SKGR is approximately 72% higher at higher transmission power. We also considered the value of

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.