In this article, we introduce a new bi-directional dual-relay selection strategy with its bit error rate (BER) performance analysis. During the first step of the proposed strategy, two relays out of a set of N relay-nodes are selected in a way to optimize the system performance in terms of BER, based on the suggested algorithm which checks if the selected relays using the max-min criterion are the best ones. In the second step, the chosen relay-nodes perform an orthogonal space-time coding scheme using the two-phase relaying protocol to establish a bi-directional communication between the communicating terminals, leading to a significant improvement in the achievable coding and diversity gain. To further improve the overall system performance, the selected relay-nodes apply also a digital network coding scheme. Furthermore, this paper discusses the analytical approximation of the BER performance of the proposed strategy, where we prove that the analytical results match almost perfectly the simulated ones. Finally, our simulation results show that the proposed strategy outperforms the current state-of-the-art ones.

The new wireless communication systems such as 5G and beyond seek to increase the data rate, decrease the latency, reduce the complexity, and extend the coverage area. However, the performance of these wireless systems are badly affected by the multiuser interference, channel impairments, multipath propagation, and time-varying fading, leading to decrease the achievable data rate and increase the bit error rate [

A relay node is an intermediate entity between the transmitter and the receiver. It receives the signal from a source-node and then processes the data by employing advanced techniques to improve the received signal to noise ratio (SNR) and achievable data rate, and to minimize the overall BER. Increasing the number of relay nodes available between the transmitter and the receiver leads to a significant enhancement in the spatial diversity using one of the relaying schemes,

Other techniques such as bi-directional communication is proposed as a solution to improve the performance in terms of BER and spectral efficiency. Those systems consist of two terminals that communicate with each other through some in-between relay nodes that are randomly distributed between them [

Some orthogonal techniques, such as STC, offer a full diversity gain with a low decoding complexity [

In recent years, many relay selection techniques have adopted to select the best one or more relay nodes out of a group of intermediate relay-nodes. In [

The motivation of this paper is that the current state-of-the-art articles are only considering the weakest or strongest channels to choose the best one or two relay-nodes,

From our simulation results, we prove that our suggested strategy offers a better performance as compared to the existing relay selection strategies. This paper is summarized as follows: Section 2 discusses the system model. Section 3 explains the BER analysis. Section 4 and Section 5 demonstrate the performance analysis. The conclusion is drawn in Section 5.

In our proposed strategy all participating relay-nodes will be performing the decode-and-forward (DF) protocol [

Given that

Note here that the relay-nodes are encountering a high decoding overhead. More specifically, the decoding complexity is increasing quadratically as the size of the constellation is getting larger, because the decoder needs to apply pairwise decoding to detect the received messages. After that, the rth relay node

where

The two relays,

To enhance the overall system’s diversity and coding gain without adding extra decoding complexity, the two selected relay-nodes

given that

In this section, we propose the mathematical analysis of the BER for our relay selection strategy, which was explained in Section 2. In this analysis, we assume, without loss of generality, that the used modulation is the binary phase shift keying (BPSK). Moreover, we suppose that the used relay stations are ideal, similarly as in [

In this proposed relaying strategy, out of N available relay stations, the

One can notice that the above expression consists of four terms where the part

Hence, the moment-generation function (MGF) of

The aforementioned expression,

Thus, the term

By combining

In a similar way,

Making use of the final expressions of

In this step, we suppose that the

where,

For the second part

Using the final expressions of

In this section, we discuss the obtained results from both Monte Carlo simulations, as well as, analytical models discussed in Section 4. In the simulations, we have assumed a wireless relay network with two single-antenna relay nodes and independent flat Rayleigh fading channels where the power is distributed among the two terminals and relays similarly as in [^{10}, the number of relays available in the network varies between two to six, and the applied modulation technique is either BPSK or 4-QAM. For fair comparison of the BER performance of all techniques, the same total transmitted power and bit rate are used.

In

Correspondingly,

In

In

In

In this article, we introduced a new two-relay selection strategy using the two-phase protocol based on STC. Furthermore, this strategy is employing a digital network coding scheme at the selected relay-nodes in order to merge the symbols into one symbol with the same constellation to reduce the power consumption of sending redundant information. By doing this, additional coding gain is achieved. In addition to that, we have proposed the analytical BER of this novel strategy and compared it with our simulation results in order to validate the proposed BER expressions. We have further proved that the performance of our new strategy outperforms the most recent strategies.