In this article, a low-cost electromagnetic structure emulating photonic nanojets is utilized to improve the efficiency of wireless relay networks. The spectral element method, due to its high accuracy, is used to verify the efficiency of the proposed structure by solving the associate field distribution. The application of optimal single-relay selection method shows that full diversity gain with low complexity can be achieved. In this paper, the proposed technique using smart relays combines the aforementioned two methods to attain the benefits of both methods by achieving the highest coding and diversity gain and enhances the overall network performance in terms of bit error rate (BER). Moreover, we analytically prove the advantage of using the proposed technique. In our simulations, it can be shown that the proposed technique outperforms the best known state-of-the-art single relay selection technique. Furthermore, the BER expressions obtained from the theoretical analysis are perfectly matched to those obtained from the conducted simulations.

In wireless communication systems, several techniques have recently been suggested to improve the overall system performance in terms of bit error rate (BER) or achievable data rate [

Spatial diversity techniques also known as multiple-input multiple-output (MIMO) techniques can improve the BER performance by sending the same information symbols several times using different transmitted antennas at the same time and frequency slots. The latter techniques are considered as being the most efficient ones since they do not require additional time or frequency slots [

Other special diversity techniques based on beamforming schemes [

In many applications, it is difficult, due to several limitations, to have many antennas on the mobile station. To solve this problem, a cooperative communication system can be performed instead of applying the conventional MIMO systems by using relay nodes distributed randomly between the transmitted antennas. These relays are used either to just amplify-and-forward (AF) the received signals or they can decode the information signals before broadcasting them to the received antenna. Therefore, in cooperative communication networks, relay-nodes will jointly process the received data messages before broadcasting them using their antennas toward the receiving entities, which will combine all the received copies from different paths to improve the spatial diversity gain. Such techniques are called the multi-antenna diversity techniques that incorporate the use of one-way or two-way relaying schemes [

Recently, many efficient relaying techniques are proposed to achieve the full diversity gain and the highest coding gain such as distributed space time coding techniques which allow the relays to apply space time coding technique to improve the overall system performance [

The previous two techniques use all relay nodes between the communicating terminals. To improve the previous techniques and achieve the full diversity gain with low decoding complexity in non-orthogonal relay-node networks and without using all relay nodes between the communicating terminals, relay selection techniques have been proposed [

In the conventional wireless relay networks, each relay node is equipped with a single antenna or several antennas to receive the signal before amplifying and forwarding it. In this paper, the received signal is improved prior to processing it by focusing the beam to the relay antenna using a specific element designed and simulated by the spectral element method (SEM) which is recently applied in electromagnetic radiation to improve the channel gain of each relay node.

In order to achieve accurate results, SEM has been utilized in this study for the computation of transmitted and scattered fields. In fact, this method has been recently applied in electromagnetic radiation and/or scattering problems due to its accuracy and the relatively lower computational requirements [

In this work, both beamforming technique emulating photonic nanojet behavior [

For our system model, we consider a one-way relay network consisting of a single-antenna transmitter

In this proposed technique, one intermediate relay node will be chosen from the R relay nodes where the optimal single relay node

After selecting the optimal relay node among all

where

where

Note here that the decoding complexity is very low, as a symbol-wise decoder which enjoys a linear decoding complexity is utilized to detect the received data messages. In DF protocol, the selected relay

The selected relay node

where

Note here that the decoding complexity is very low, as a symbol-wise decoder which enjoys a linear decoding complexity is being used to detect the received data messages.

The computational domain consists of a lossy dielectric hemi-cylinder (whose radius is Ri and complex permittivity is

in which;

The field governed by the above equation decays rapidly as it propagates from the source location. That is; the assumption of such a radiating source is put in order to imitate the real situation of transmitting antenna in GHz ranges. The following frequency-domain Helmholtz equation must be satisfied inside the computational domain (except the PML):

where

Measurements of complex permittivity for several types of materials at wide range of frequencies have been performed in many studies [

In

As it can be clearly seen from the

As explained in the manuscript, we propose the addition of a hemi-cylindrical object (with a realistic complex permittivity values) that focuses the incident wave and hence amplifies the signal before it is just received by the wireless relay at communication frequency ranges. This focusing technique is emulated from photonic nanojets at optical frequencies. In order to verify the design, electromagnetic simulation is required to show that the field magnitudes are increased due to this proposed structure. The field magnitude is then used to prove that BER is decreased.

For this structure to be well utilized, the antenna of the receiver must be placed in the region where the wave focusing takes place. Fortunately, the focal point has almost stationary position and is dependent on material permittivity. Another important fact is that, if the transmitting source change its location over a range of around 30 degrees, the corresponding the focal point stays within the axis where the receiving antenna exists. The last two points in addition to others reported for photonic jets [

In this section, the mathematical BER expression of the proposed smart relay selection strategy is discussed. Let us first consider the assumptions discussed in Section 2 and assume that the information symbols are drawn from binary phase shift keying (BPSK) constellation. Similar to [

In our suggested strategy, the proposed relay selection technique based on the max-min criteria explained in

where

In this section, we introduce the simulation results as well as the analytical results proposed in Section 5.

From

In this article, generation of photonic nanojet at optical frequencies resulted from illumination of lossless dielectric micro-cylinders is emulated for wireless networks frequencies. That is; we merged both, beamforming approach, and the optimal single-relay selection approach that is applied in wireless relay network, in the proposed strategy to get the benefits of both approaches. The beamforming approach calculated by SEM is modified to calculate the efficiency of the relay nodes while the relay selection method is improved to achieve the full diversity gain. Therefore, in this paper, an enhanced single relay selection strategy is introduced to be used for wireless relay networks using smart relays that offer higher coding gain and enjoy full diversity gain to improve the overall network performance in terms of BER. Furthermore, we proved the advantage of the proposed strategy analytically and through simulations. In our simulations, we show that our proposed strategy outperforms the best known state-of-the-art single relay selection technique. Furthermore, we proved that the BER results obtained from our conducted simulations are perfectly match those obtained from the theoretical analysis.