Computers, Materials & Continua DOI:10.32604/cmc.2022.030371 | |

Article |

A Beamforming Technique Using Rotman Lens Antenna for Wireless Relay Networks

College of Engineering and Technology, American University of the Middle East, Kuwait

*Corresponding Author: Samer Alabed. Email: samer.al-abed@aum.edu.kw

Received: 24 March 2022; Accepted: 27 May 2022

Abstract: Rotman lens, which is a radio frequency beam-former that consists of multiple input and multiple output beam ports, can be used in industrial, scientific, and medical applications as a beam steering device. The input ports collect the signals to be propagated through the lens cavity toward the output ports before being transmitted by the antenna arrays to the destination in order to enhance the error performance by optimizing the overall signal to noise ratio (SNR). In this article, a low-cost Rotman lens antenna is designed and deployed to enhance the overall performance of the conventional cooperative communication systems without needing any additional power, extra time or frequency slots. In the suggested system, the smart Rotman lens antennas generate a beam steering in the direction of the destination to maximize the received SNR at the destination by applying the proposed optimal beamforming technique. The suggested optimal beamforming technique enjoys high diversity, as well as, low encoding and decoding complexity. Furthermore, we proved the advantages of our suggested strategy through both theoretical results and simulations using Monte Carlo runs. The Monte Carlo simulations show that the suggested strategy enjoys better error performance compared to the current state-of-the-art distributed multi-antenna strategies. In addition, the bit error rate (BER) curves drawn from the analytical results are closely matching to those drawn from our conducted Monte Carlo simulations.

Keywords: Performance analysis; smart antenna; Rotman lens antenna; multi-antenna systems; wireless relay networks cooperative diversity schemes; digital network coding; relay selection schemes

In the recent years, several techniques have been proposed in the field of wireless communications to enhance the error performance of the whole system and its achievable throughput [1–6]. A group of these techniques works by increasing or optimizing the transmitted power, while another group is applying powerful forward error detection and correction techniques to increase the achievable gain. Latest techniques are using time, frequency, and space-diversity techniques in order to enhance the total diversity gain [7–12]. In time diversity, the BER performance can be improved by sending the same signal many times in several time periods [13–16]. While, in frequency diversity the error performance is enhanced by sending the same signal many times in several frequency bands. Also, space diversity schemes that are known as multiple input multiple output (MIMO) schemes can be used to enhance the error performance by broadcasting the same signal many times via different transmitting antennas using the same frequency band and time period, leading to the most powerful performance without requiring extra periods or frequency bands [17,18]. Later on, several schemes are suggested to improve both diversity order and coding gain by combining diversity techniques with coding algorithms including but not limited to space-frequency coding (SFC) schemes and space-time coding (STC) schemes [10,13–15]. Furthermore, special diversity techniques using beamforming schemes [11–12,17–19] are used to steer the transmitting antenna beams towards the destination terminal to enhance the BER performance and the throughput by maximizing the received signal to noise ratio (SNR), given that the BER performance of the multi-antenna systems suffer from the multiuser interference and channel impairments [1–9]. In addition, it is very well known that it is difficult to deploy several antennas at the same mobile station due to several limitations. Therefore, cooperative communication systems can be used to overcome this problem by randomly distributing a group of relay nodes between the two communicating parties [5–11,20,21]. Those relay nodes can be used in two modes of operation, either to amplify and forward (AF) the obtained signals or to detect the transmitted symbols before forwarding them to the receiving antennas. However, relay-nodes in wireless relay systems process the obtained signals before transmitting them to the destination terminals by merging the obtained copies of the transmitted signal received via several links to enhance the diversity order and coding gain. These schemes are well known as the spatial-diversity schemes [5–11]. Lately, several improved relaying methods have been introduced to obtain a high diversity and coding gain. For instance, the so called space-time diversity schemes for cooperative communication systems, in which the relay nodes are applying a space-time coding techniques, are found to enhance the performance in terms of BER and achievable data rate [9,13–15,22]. The distributed beamforming techniques, where the relay nodes are capable of forming a beam towards the destination to enhance the achievable SNR, are introduced in [9,11,12,23–25]. More specifically, the authors of [17] proposed a new beamforming approach by combining a single-group multicasting network with orthogonal space-time block coding in order to minimize the total transmitted power while maintaining the quality of service constraints. Article [11] proposed a new non-coherent beam-forming scheme for bi-directional cooperative communication systems where the angles of the obtained signals on the relay nodes are adjusted without needing CSI or training signals. In [24], a non-trivial combination between the differential diversity and the distributed beamforming techniques have been used to develop a simple distributed differential transmit beamforming technique that does not require CSI at any node while providing high BER, optimal end-to-end delay, and low decoding complexity. A bi-directional differential beamforming scheme have been proposed in [9] by utilizing differential phase shift keying modulation at the relay stations to enable beamforming without the knowledge of any instantaneous CSI. On the other hand, more non-beamforming techniques have been proposed without the knowledge of any instantaneous CSI [26–29]. The Rotman lens is a radio frequency (RF) beam-former that has multi-input and multi-output beam ports [30,31]. The input ports collect the RF signals to be propagated through the lens cavity toward the output ports before being transmitted by the antenna arrays [30]. The authors of [32] emphasize on the need to combine the use of Rotman lens with RF switching for superior performance compared to conventional phased arrays. One great advantage of Rotman lens is its capability to generate many beams without the need to physically moving the antenna system [33], therefore, its being widely used in the radar surveillance systems to see targets in multiple directions without changing the orientation of the antenna. Also, in [34] the authors found that using the low-cost Rotman lens in hybrid beamforming systems can achieve a superior performance, exhibit wideband capability compared to the high-cost phase shifters and the small-scale MIMO systems. In this article, a low-cost Rotman lens antenna is utilized in order to enhance the overall performance of the conventional cooperative communication systems without needing any additional power, extra time or frequency slots. In the suggested system, the smart Rotman lens antennas generate a beam steering in the direction of the destination to maximize the received SNR by applying the proposed optimal beamforming technique. The suggested optimal beamforming technique enjoys high diversity order and low encoding and decoding complexity. Furthermore, we proved the advantages of our suggested strategy through both theoretical results and simulations using Monte Carlo runs. The Monte Carlo simulations show that the suggested strategy enjoys better BER performance compared to the current distributed multi-antenna strategies. In addition, the BER curves drawn from the analytical results are closely matching those drawn from our conducted Monte Carlo simulations.

Given that the Rotman lens is considered as a radio-frequency beam former that consists of N input terminals and M output terminals [30]. The received signals at the N input terminals will flow via the Rotman-lens to the M output terminals before reaching the transmitting antennas. The required phase and amplitude distributions can be obtained using the formulas of the optical path length equality by calculating the needed locations of the input and output terminals, and the transmission-line lengths as well. Rotman lens is capable of producing a steering beam of different phases by exciting the corresponding input/output ports, as well as, producing multiple beams by exciting the multiple input/output ports simultaneously. The use of Rotman lens is an efficient way to design low-cost smart antennas as it provides a true time delay leading to a larger spectrum, and a low insertion loss allowing to be easily fabricated at low cost [30].

In our proposed cooperative communication system, a unidirectional network composed of a transmitter

3 The Proposed Beamforming Technique Using Rotman Lens Antenna

The relationship between the input signal vector and the output signal vector is characterized by the Rotman lens matrix as given in the below equations:

where

where

where

where

Here, the signal is represented by the term

Given that the Rotman lens is going to adjust the phase shifts of all the received signals to optimize the SNR at the destination. Moreover, we assume that

Leading to SNR at the receiver side given as:

where

Now, in order to maximize

Also, the power scaling factor

where

Therefore, during the second phase, the received signal can be written as:

Using the maximum likelihood (ML) technique to decode the information at the receiver side as per the below equation:

Where

In this section, using the assumptions presented in Section 2 and without any prior channel knowledge in the whole system, the analytical BER performance of the suggested technique is introduced. For simplicity, we will consider that

where

Here,

Now, the average BER, calculated through finding the average of the conditional formula

where

Where

where

Substituting

where

If a large SNR is considered, i.e.,

This section presents the analytical and simulated performance results explained before in Section 4. Figs. 3, 4 and 5 show the BER performance of the cooperative communication system shown in Fig. 1 which has a single transmitter

Fig. 5 considers the scenario when we have a cooperative communication system using only one relay carrying one smart Rotman antenna and a direct channel from the source to destination is considered. Fig. 5 shows the analytical and simulated performance in terms of BER of the suggested technique at the destination using 4-PSK modulation. Moreover, Fig. 5 clearly shows that the performance in terms of BER using Monte Carlo simulation of the suggested strategy matches the analytical performance in terms of BER calculated using the formulas given in Section 4. From Figs. 3, 4 and 5, we can clearly observe that our proposed strategy outperforms all the best-known strategies [9–14].

In this article, a low-cost Rotman lens antenna is utilized in order to enhance the performance of the conventional cooperative communication networks without requiring any extra power, or additional time or frequency slots. In the suggested system, the smart Rotman lens antennas form a beam in the direction of the destination to maximize the received SNR at the destination by performing optimal beamforming technique. The suggested optimal beamforming technique enjoys high diversity order and low encoding and decoding complexity. Furthermore, we proved the advantages of our suggested strategy through both theoretical results and simulations using Monte Carlo runs. The Monte Carlo simulations show that the suggested strategy enjoys better BER performance as compared to the current state-of-the-art distributed multi-antenna strategies. In addition, the BER curves drawn from the analytical results are closely matching to those drawn from our conducted Monte Carlo simulations.

Funding Statement: The article has been supported by the College of Engineering and Technology, American University of the Middle East, Kuwait. Homepage: https://www.aum.edu.kw.

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

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